{"id":36897,"date":"2024-03-29T17:37:46","date_gmt":"2024-03-29T17:37:46","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=36897"},"modified":"2024-03-29T17:45:04","modified_gmt":"2024-03-29T17:45:04","slug":"perimetr-ploshhad-i-obem","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/perimetr-ploshhad-i-obem\/","title":{"rendered":"\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c"},"content":{"rendered":"\n<h3 class=\"has-text-align-center wp-block-heading\"><strong>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>\u041a\u0430\u043a \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043b\u0438\u043d\u0435\u0439\u043a\u0438 \u0438 \u0446\u0438\u0440\u043a\u0443\u043b\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438?&nbsp;<\/li><li>\u041f\u043e\u0447\u0435\u043c\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0438 \u043e\u0431\u044a\u0435\u043c \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0431\u0443\u043a\u0432\u0430\u043c\u0438 P, S \u0438 V?<\/li><li>\u0410 \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430?<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u043b\u0438\u0441\u044c \u043d\u0430\u043c \u043d\u0430 \u043f\u0440\u043e\u0442\u044f\u0436\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0432 \u0448\u043a\u043e\u043b\u0435. \u0414\u0430 \u0438 \u0432 \u0436\u0438\u0437\u043d\u0438 \u043e\u043d\u0438 \u043d\u0430\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f, \u0432\u0435\u0434\u044c \u043c\u044b \u0436\u0438\u0432\u0435\u043c \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435. \u041d\u0430\u0441\u0442\u0430\u043b \u043c\u043e\u043c\u0435\u043d\u0442 \u0441\u043e\u0431\u0440\u0430\u0442\u044c \u0432\u0441\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u0432\u043e\u0435\u0434\u0438\u043d\u043e \u0438 \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u044f \u043d\u0430 \u044d\u0442\u0438 \u0442\u0435\u043c\u044b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u043e \u043f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043d\u0430\u0447\u043d\u0435\u043c, \u0432\u043e\u0442 \u0441\u0441\u044b\u043b\u043a\u0438 \u043d\u0430 \u0441\u0442\u0430\u0442\u044c\u0438 \u043f\u043e \u0444\u0438\u0433\u0443\u0440\u0430\u043c \u0438 \u0442\u0435\u043b\u0430\u043c, \u043f\u0440\u043e \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0431\u0443\u0434\u0435\u043c \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/umschool.net\/library\/matematika\/treugolnik\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/parallelogramm\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/trapecziya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0430\u043f\u0435\u0446\u0438\u044f<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/mnogougolniki\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041c\u043d\u043e\u0433\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/okruzhnost-i-krug\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/prizma\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041f\u0440\u0438\u0437\u043c\u0430<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/piramida\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041f\u0438\u0440\u0430\u043c\u0438\u0434\u0430<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/czilindr\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0426\u0438\u043b\u0438\u043d\u0434\u0440<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/konus\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041a\u043e\u043d\u0443\u0441<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/shar\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0428\u0430\u0440<\/a><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a, \u0441 \u044d\u0442\u0438\u043c \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c. \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u043c \u043a \u043d\u0430\u0448\u0435\u0439 \u0442\u0435\u043c\u0435!&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440\"><strong>\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0441\u0435 \u043c\u044b \u0435\u0449\u0435 \u0432 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0439 \u0448\u043a\u043e\u043b\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u043b\u0438, \u0447\u0442\u043e <strong>\u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440<\/strong> \u2014 \u0441\u0443\u043c\u043c\u0430 \u0434\u043b\u0438\u043d \u0432\u0441\u0435\u0445 \u0441\u0442\u043e\u0440\u043e\u043d. \u042d\u0442\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0444\u0438\u0433\u0443\u0440, \u043a\u0440\u043e\u043c\u0435 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438. \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0438\u0437 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041a\u0432\u0430\u0434\u0440\u0430\u0442:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = 4a\\)<\/li><li>\\(P = 2\\sqrt{2d}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430, <em>d<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = 2(a+b)\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = 2(a+b)\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u2014 \u0447\u0430\u0441\u0442\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440\u044b \u0441\u0447\u0438\u0442\u0430\u044e\u0442\u0441\u044f \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0422\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = a+b+c\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em>, <em>b<\/em> \u0438 <em>c<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = 2\\pi r\\)<\/li><li>\\(P =\\pi d\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>r<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, <em>d<\/em> \u2014 \u0434\u0438\u0430\u043c\u0435\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u2014 \u0447\u0438\u0441\u043b\u043e \u043f\u0438, \u0440\u0430\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 3,14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0422\u0440\u0430\u043f\u0435\u0446\u0438\u044f:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = a+b+c+d\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439 \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438, <em>c<\/em> \u0438 <em>d<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u0441\u0442\u043e\u0440\u043e\u043d \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0420\u043e\u043c\u0431:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(P = 4a\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0440\u043e\u043c\u0431\u0430.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041a\u0430\u043a \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043b\u0438\u043d\u0435\u0439\u043a\u0438 \u0438 \u0446\u0438\u0440\u043a\u0443\u043b\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438?\u00a0<\/strong><br><br>\u0421\u043f\u043e\u0439\u043b\u0435\u0440: \u043d\u0438\u043a\u0430\u043a. \u042d\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443\u0440\u043e\u0439 \u043a\u0440\u0443\u0433\u0430, \u0438 \u043e\u043d\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0441\u0430\u043c\u044b\u0445 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043d\u0435\u0440\u0430\u0437\u0440\u0435\u0448\u0438\u043c\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0438\u0440\u043a\u0443\u043b\u044f \u0438 \u043b\u0438\u043d\u0435\u0439\u043a\u0438.\u00a0<br><br>\u041d\u0430\u0434 \u043d\u0435\u0439 \u0431\u0438\u043b\u0438\u0441\u044c \u0441\u043e\u0442\u043d\u0438 \u043b\u0435\u0442 \u0442\u0430\u043a\u0438\u0435 \u0443\u0447\u0435\u043d\u044b\u0435, \u043a\u0430\u043a \u0410\u0440\u0445\u0438\u043c\u0435\u0434, \u0424\u0438\u0431\u043e\u043d\u0430\u0447\u0447\u0438, \u0434\u0430 \u0412\u0438\u043d\u0447\u0438, \u0413\u044e\u0439\u0433\u0435\u043d\u0441 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435. \u041d\u0438\u043a\u043e\u043c\u0443 \u0442\u0430\u043a \u0438 \u043d\u0435 \u0443\u0434\u0430\u043b\u043e\u0441\u044c \u0440\u0435\u0448\u0438\u0442\u044c \u044d\u0442\u0443 \u0437\u0430\u0434\u0430\u0447\u0443. \u0412 1882 \u0433\u043e\u0434\u0443 \u041b\u0438\u043d\u0434\u0435\u043c\u0430\u043d, \u043d\u0435\u043c\u0435\u0446\u043a\u0438\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a, \u0434\u043e\u043a\u0430\u0437\u0430\u043b \u043d\u0435\u0440\u0430\u0437\u0440\u0435\u0448\u0438\u043c\u043e\u0441\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443\u0440\u044b \u043a\u0440\u0443\u0433\u0430.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430<strong> \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0432 \u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u21161.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0412 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0435\u0439 \u0434\u043e \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0435\u0433\u043e \u0441\u0442\u043e\u0440\u043e\u043d \u0440\u0430\u0432\u043d\u043e 10. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u044d\u0442\u043e\u0433\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430.<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/1-1024x1024.jpg\" alt=\"\" class=\"wp-image-36904\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/1-1024x1024.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/1-300x300.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/1-150x150.jpg 150w, \/library\/wp-content\/uploads\/2024\/03\/1-768x769.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/1.jpg 1184w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041f\u043e\u0434 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435\u043c \u043e\u0431\u044b\u0447\u043d\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u044e\u0442 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u0441\u0442\u043e\u0440\u043e\u043d\u044b. \u0421\u043e\u0435\u0434\u0438\u043d\u0438\u043c \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043e\u043c \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0435\u0439 \u0438 \u0441\u0442\u043e\u0440\u043e\u043d\u0443:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/2-1024x1024.jpg\" alt=\"\" class=\"wp-image-36905\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/2-1024x1024.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/2-300x300.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/2-150x150.jpg 150w, \/library\/wp-content\/uploads\/2024\/03\/2-768x769.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/2.jpg 1184w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u041a\u0430\u043a \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u043f\u043e\u043b\u0443\u0447\u0438\u0432\u0448\u0435\u0439\u0441\u044f \u043e\u0442\u0440\u0435\u0437\u043e\u043a OK \u0440\u0430\u0432\u0435\u043d \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b. \u0417\u043d\u0430\u0447\u0438\u0442, \u0441\u0442\u043e\u0440\u043e\u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430 \u0440\u0430\u0432\u043d\u0430 20. \u041d\u0430\u0439\u0434\u0435\u043c \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440:<br><br>\\(P = 4a\\)<br>\\(P = 4*20 = 80\\)<br><br><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> 80<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421 \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440\u0430\u043c\u0438 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c, \u0442\u0435\u043f\u0435\u0440\u044c \u043f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u043f\u043b\u043e\u0449\u0430\u0434\u044f\u043c.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u041c\u0435\u0442\u043e\u0434-\u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439\"><strong>\u041c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439<\/strong><\/h2>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041f\u043b\u043e\u0449\u0430\u0434\u044c<\/strong> \u2014 \u043c\u0435\u0440\u0430 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u0444\u0438\u0433\u0443\u0440\u0430 \u0432\u043d\u0443\u0442\u0440\u0438 \u0441\u0432\u043e\u0438\u0445 \u0433\u0440\u0430\u043d\u0438\u0446. \u0418\u0437\u043c\u0435\u0440\u044f\u0435\u0442\u0441\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0441\u0430\u043d\u0442\u0438\u043c\u0435\u0442\u0440\u0430\u0445 (\u0441\u043c2), \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u0435\u0442\u0440\u0430\u0445 (\u043c2), \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043a\u0438\u043b\u043e\u043c\u0435\u0442\u0440\u0430\u0445 (\u043a\u043c2) \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0438\u0437 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041a\u0432\u0430\u0434\u0440\u0430\u0442:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S = a^2\\)<\/li><li>\\(S =\\frac{1}{2}d^2\\)<\/li><li>\\(S = 4r^2\\)<\/li><li>\\(S = 2R^2\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430, <em>d<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430, <em>r<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 <a href=\"https:\/\/umschool.net\/library\/matematika\/vpisannaya-i-opisannaya-okruzhnost\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0432\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438<\/a>, <em>R<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 <a href=\"https:\/\/umschool.net\/library\/matematika\/vpisannaya-i-opisannaya-okruzhnost\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043e\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S = ab\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0422\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S =\\frac{1}{2}ah\\). \u0417\u0434\u0435\u0441\u044c \u0432\u0430\u0436\u043d\u043e, \u0447\u0442\u043e \u0432\u044b\u0441\u043e\u0442\u0430 <em>h<\/em> \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0430 \u0438\u043c\u0435\u043d\u043d\u043e \u043a \u0441\u0442\u043e\u0440\u043e\u043d\u0435 <em>a<\/em>.\u00a0<\/li><li>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0413\u0435\u0440\u043e\u043d\u0430: \\(S =\\sqrt{p(p-a)(p-b)(p-c)}\\)<\/li><li>\\(S =\\frac{1}{2}ab*sin(\u03b3)\\)<\/li><li>\\(S = pr\\)<\/li><li>\\(S =\\frac{abc}{4R}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em>, <em>b<\/em> \u0438 <em>c<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, <em>p<\/em> \u2014 \u043f\u043e\u043b\u0443\u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, <em>\u03b3<\/em> \u2014 \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c\u0438 <em>a <\/em>\u0438<em> b, r \u2014 <\/em>\u0440\u0430\u0434\u0438\u0443\u0441 \u0432\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, <em>R<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S =\\pi r^2\\)<\/li><li>\\(S =\\frac{1}{4}d^2\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>r<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, <em>d<\/em> \u2014 \u0434\u0438\u0430\u043c\u0435\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u2014 \u0447\u0438\u0441\u043b\u043e \u043f\u0438, \u0440\u0430\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 3,14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0422\u0440\u0430\u043f\u0435\u0446\u0438\u044f:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S =\\frac{1}{2}(a+b)h\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439 \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430 \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S =ah\u00a0\\)<\/li><li>\\(S = ab*sin(\u03b1)\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u0438 <em>b<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0441\u0442\u043e\u0440\u043e\u043d \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430, <em>\u03b1<\/em> \u2014 \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c\u0438 <em>a <\/em>\u0438 <em>b<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0420\u043e\u043c\u0431:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(S = ah\\)<\/li><li>\\(S =\\frac{1}{2}d_1d_2\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0440\u043e\u043c\u0431\u0430, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430 \u0440\u043e\u043c\u0431\u0430,<strong> <\/strong>\\(d_1\\) \u0438 \\(d_2\\) \u2014 \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u0440\u043e\u043c\u0431\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0442\u0430\u043a, \u043c\u044b \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043b\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b. \u041d\u043e \u043c\u044b \u0442\u0430\u043a \u0438 \u043d\u0435 \u0443\u0437\u043d\u0430\u043b\u0438, \u0447\u0442\u043e \u0436\u0435 \u0442\u0430\u043a\u043e\u0435 \u043c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439.<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439<\/strong> \u2014 \u043c\u0435\u0442\u043e\u0434 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0444\u0438\u0433\u0443\u0440 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c <strong>\u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430<\/strong> \u043c\u0435\u0442\u043e\u0434\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u0415\u0441\u043b\u0438 \u0432\u0435\u0440\u0448\u0438\u043d\u0443 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u043f\u0435\u0440\u0435\u0434\u0432\u0438\u0433\u0430\u0442\u044c \u043f\u043e \u043f\u0440\u044f\u043c\u043e\u0439, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044e, \u0442\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043d\u0435 \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u0441\u044f.<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-23-1024x586.jpeg\" alt=\"\" class=\"wp-image-36908\" width=\"256\" height=\"147\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-23-1024x586.jpeg 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-23-300x172.jpeg 300w, \/library\/wp-content\/uploads\/2024\/03\/image-23-768x439.jpeg 768w, \/library\/wp-content\/uploads\/2024\/03\/image-23.jpeg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u0415\u0441\u043b\u0438 \u0434\u0432\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435 \u0432\u044b\u0441\u043e\u0442\u044b, \u0442\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u0438\u0445 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0440\u0430\u0432\u043d\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u0434\u043b\u0438\u043d \u0441\u0442\u043e\u0440\u043e\u043d, \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0443\u0449\u0435\u043d\u044b \u044d\u0442\u0438 \u0432\u044b\u0441\u043e\u0442\u044b.<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-24-1024x652.jpeg\" alt=\"\" class=\"wp-image-36909\" width=\"256\" height=\"163\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-24-1024x652.jpeg 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-24-300x191.jpeg 300w, \/library\/wp-content\/uploads\/2024\/03\/image-24-768x489.jpeg 768w, \/library\/wp-content\/uploads\/2024\/03\/image-24.jpeg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(\\frac{S_1}{S_2}=\\frac{a}{b}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e:<\/strong> \u041f\u0443\u0441\u0442\u044c \\(h_1=h_2\\), \u0442\u043e\u0433\u0434\u0430 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\frac{S_1}{S_2}=\\frac{\\frac{1}{2}*a*h_1}{\\frac{1}{2}*b*h_2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u0441\u043b\u0435 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0438\u044f \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\frac{S_1}{S_2}=\\frac{a}{b}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a \u0436\u0435 \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\u0415\u0441\u043b\u0438 \u0434\u0432\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0442\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0440\u0430\u0432\u043d\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u0432\u044b\u0441\u043e\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043a \u044d\u0442\u0438\u043c \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u044b.<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/5-1024x833.jpg\" alt=\"\" class=\"wp-image-36910\" width=\"256\" height=\"208\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/5-1024x833.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/5-300x244.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/5-768x625.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/5.jpg 1112w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(\\frac{S_1}{S_2}=\\frac{h_1}{h_2}\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>\u0423 \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0445 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0440\u0430\u0432\u043d\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430 \u043f\u043e\u0434\u043e\u0431\u0438\u044f.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043f\u043e\u0434\u043e\u0431\u0438\u044f<\/strong> \u2014 \u0447\u0438\u0441\u043b\u043e <em>k<\/em>, \u0440\u0430\u0432\u043d\u043e\u0435 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u0441\u0445\u043e\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0441\u0442\u043e\u0440\u043e\u043d \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0445 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432. \u041e\u0431 \u044d\u0442\u043e\u043c \u043c\u044b \u0440\u0430\u0441\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u043b\u0438 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/umschool.net\/library\/matematika\/ravenstvo-i-podobie-treugolnikov\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u0440\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0438 \u043f\u043e\u0434\u043e\u0431\u0438\u0435 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-25-1024x549.jpeg\" alt=\"\" class=\"wp-image-36912\" width=\"256\" height=\"137\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-25-1024x549.jpeg 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-25-300x161.jpeg 300w, \/library\/wp-content\/uploads\/2024\/03\/image-25-768x412.jpeg 768w, \/library\/wp-content\/uploads\/2024\/03\/image-25.jpeg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(\\frac{S_1}{S_2}=k^2\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\"><li>\u0412\u0441\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0434\u0435\u043b\u044f\u0442 \u0435\u0433\u043e \u043d\u0430 \u0447\u0435\u0442\u044b\u0440\u0435 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u0443 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0440\u0430\u0432\u043d\u044b\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u0438.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u0421\u0440\u0435\u0434\u043d\u044f\u044f \u043b\u0438\u043d\u0438\u044f \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430<\/strong> \u2014 \u043e\u0442\u0440\u0435\u0437\u043e\u043a, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u0435\u0442 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b \u0434\u0432\u0443\u0445 \u0441\u0442\u043e\u0440\u043e\u043d.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-26-1024x1024.jpeg\" alt=\"\" class=\"wp-image-36913\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-26-1024x1024.jpeg 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-26-300x300.jpeg 300w, \/library\/wp-content\/uploads\/2024\/03\/image-26-150x150.jpeg 150w, \/library\/wp-content\/uploads\/2024\/03\/image-26-768x768.jpeg 768w, \/library\/wp-content\/uploads\/2024\/03\/image-26.jpeg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(S_1=S_2=S_3=S_4=\\frac{1}{4}S\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\"><li>\u0415\u0441\u043b\u0438 \u0434\u0432\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0438\u043c\u0435\u044e\u0442 \u043f\u043e \u0440\u0430\u0432\u043d\u043e\u043c\u0443 \u0443\u0433\u043b\u0443, \u0442\u043e \u0438\u0445 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0441\u0442\u043e\u0440\u043e\u043d, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0437\u0430\u043a\u043b\u044e\u0447\u0430\u044e\u0442 \u044d\u0442\u0438 \u0443\u0433\u043b\u044b.<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-27-1024x1024.jpeg\" alt=\"\" class=\"wp-image-36914\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-27-1024x1024.jpeg 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-27-300x300.jpeg 300w, \/library\/wp-content\/uploads\/2024\/03\/image-27-150x150.jpeg 150w, \/library\/wp-content\/uploads\/2024\/03\/image-27-768x768.jpeg 768w, \/library\/wp-content\/uploads\/2024\/03\/image-27.jpeg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(\\frac{S_{ABC}}{S_{MBN}}=\\frac{AB*BC}{MB*BN}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u0447\u0443, \u0447\u0442\u043e\u0431\u044b \u043e\u0442\u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u043c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439.<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0422\u0430\u043a\u043e\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430<strong> \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0432 \u211617. \u0420\u0435\u0448\u0438\u043c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0443\u043d\u043a\u0442 \u0430.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 AC \u0438 BD \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438 ABCD \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0432 \u0442\u043e\u0447\u043a\u0435 O, BC \u0438 AD\u202f\u202f\u2014 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438.<\/em><br><br><em>\u0430) \u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e <\/em>\\(\\frac{S_{DOC}}{S_{AOD}}=\\frac{BC}{AD}\\)<br><em>\u0431) \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438, \u0435\u0441\u043b\u0438 <\/em>\\(AD\u202f\u202f=\u202f\u202f4BC, S_{OCD} = 2\\)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/9-1024x631.jpg\" alt=\"\" class=\"wp-image-36919\" width=\"256\" height=\"158\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/9-1024x631.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/9-300x185.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/9-768x473.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/9.jpg 1188w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u0430) \u0423 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 AOD \u0438 DOC \u0435\u0441\u0442\u044c \u043e\u0431\u0449\u0430\u044f \u0432\u044b\u0441\u043e\u0442\u0430, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0438\u0437 \u0432\u0435\u0440\u0448\u0438\u043d\u044b D. \u0417\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0438\u0445 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u0442\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \u043a \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0430 \u0432\u044b\u0441\u043e\u0442\u0430, \u043a\u0430\u043a \u044d\u0442\u043e \u0431\u044b\u043b\u043e \u0432 \u043d\u0430\u0448\u0435\u043c \u0432\u0442\u043e\u0440\u043e\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0435 \u043c\u0435\u0442\u043e\u0434\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/10-1024x629.jpg\" alt=\"\" class=\"wp-image-36920\" width=\"256\" height=\"157\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/10-1024x629.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/10-300x184.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/10-768x472.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/10.jpg 1182w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0417\u043d\u0430\u0447\u0438\u0442, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<br><br>\\(\\frac{S_{DOC}}{S_{AOD}}=\\frac{CO}{AO}\\)<br><br>\u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438 <em>AOD <\/em>\u0438 <em>BOC<\/em>. \u0423\u0433\u043e\u043b <em>CAD <\/em>\u0440\u0430\u0432\u0435\u043d \u0443\u0433\u043b\u0443 <em>BCA<\/em>, \u0430 \u0443\u0433\u043e\u043b <em>ADB <\/em>\u0440\u0430\u0432\u0435\u043d \u0443\u0433\u043b\u0443 <em>CBD<\/em>, \u0442\u0430\u043a \u043a\u0430\u043a \u043e\u043d\u0438 \u043d\u0430\u043a\u0440\u0435\u0441\u0442 \u043b\u0435\u0436\u0430\u0449\u0438\u0435: <em>BC <\/em>\u0438 <em>AD <\/em>\u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0442\u0430\u043a \u043a\u0430\u043a \u044d\u0442\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u0438, \u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0438 <em>AC <\/em>\u0438 <em>BD <\/em>\u2014 \u0441\u0435\u043a\u0443\u0449\u0438\u0435. \u041f\u043e\u0432\u0442\u043e\u0440\u0438\u0442\u044c \u0442\u0435\u043c\u0443 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u0440\u044f\u043c\u044b\u0445 \u043c\u043e\u0436\u0435\u0442\u0435 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u043e <a href=\"https:\/\/umschool.net\/library\/matematika\/osnovy-planimetrii-tochka-pryamaya-luch-otrezok-i-ugol\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043e\u0441\u043d\u043e\u0432\u044b \u043f\u043b\u0430\u043d\u0438\u043c\u0435\u0442\u0440\u0438\u0438<\/a>.\u00a0<br><br>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438 <em>AOD <\/em>\u0438 <em>BOC <\/em>\u043f\u043e\u0434\u043e\u0431\u043d\u044b. \u0417\u043d\u0430\u0447\u0438\u0442,\u00a0<br><br>\\(\\frac{BC}{AD}=\\frac{CO}{OA}=\\frac{BO}{OD}\\)<br><br>\u0422\u0430\u043a \u043a\u0430\u043a \\(\\frac{S_{DOC}}{S_{AOD}}=\\frac{CO}{AO}\\) \u0438 \\(\\frac{BC}{AD}=\\frac{CO}{OA}\\), \u0442\u043e \\(\\frac{S_{DOC}}{S_{AOD}}=\\frac{BC}{AD}\\). <br>\u0427\u0442\u043e \u0438 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043b\u043e\u0441\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421 \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c, \u043e\u0441\u0442\u0430\u043b\u043e\u0441\u044c \u0441\u0430\u043c\u043e\u0435 \u043d\u0430 \u043f\u0435\u0440\u0432\u044b\u0439 \u0432\u0437\u0433\u043b\u044f\u0434 \u0441\u043b\u043e\u0436\u043d\u043e\u0435 \u2014 \u043c\u0435\u0442\u043e\u0434 \u043e\u0431\u044a\u0435\u043c\u043e\u0432.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u041c\u0435\u0442\u043e\u0434-\u043e\u0431\u044a\u0451\u043c\u043e\u0432\">\u041c\u0435\u0442\u043e\u0434 \u043e\u0431\u044a\u0451\u043c\u043e\u0432<\/h2>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041e\u0431\u044a\u0435\u043c<\/strong> \u2014 \u043c\u0435\u0440\u0430 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u0435\u043b\u043e \u0432\u043d\u0443\u0442\u0440\u0438 \u0441\u0432\u043e\u0438\u0445 \u0433\u0440\u0430\u043d\u0438\u0446. \u0418\u0437\u043c\u0435\u0440\u044f\u0435\u0442\u0441\u044f \u0432 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0430\u043d\u0442\u0438\u043c\u0435\u0442\u0440\u0430\u0445 (\\(\u0441\u043c^3\\)), \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043c\u0435\u0442\u0440\u0430\u0445 (\\(\u043c^3\\)) \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041f\u043e\u0447\u0435\u043c\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0438 \u043e\u0431\u044a\u0435\u043c \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0431\u0443\u043a\u0432\u0430\u043c\u0438 P, S \u0438 V?<\/strong><br><br>\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0437\u0430\u0433\u043b\u0430\u0432\u043d\u043e\u0439 \u043b\u0430\u0442\u0438\u043d\u0441\u043a\u043e\u0439 \u0431\u0443\u043a\u0432\u043e\u0439 P, \u0442\u0430\u043a \u043a\u0430\u043a \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0430\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u043e\u0433\u043e \u0441\u043b\u043e\u0432\u0430 Perimeter. \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u2014 \u043b\u0430\u0442\u0438\u043d\u0441\u043a\u043e\u0439 \u0431\u0443\u043a\u0432\u043e\u0439 S, \u0442\u0430\u043a \u043a\u0430\u043a \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0441\u043b\u043e\u0432\u0430 Square. \u0410 \u043e\u0431\u044a\u0435\u043c \u2014 \u043b\u0430\u0442\u0438\u043d\u0441\u043a\u043e\u0439 \u0431\u0443\u043a\u0432\u043e\u0439 V, \u0442\u0430\u043a \u043a\u0430\u043a \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 Volume.\u00a0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043e\u0431\u044a\u0435\u043c\u0430 \u0438 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u0438\u0437 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041a\u0443\u0431:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V = a^3\\)<\/li><li>\\(S = 6a^2\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0440\u0435\u0431\u0440\u0430 \u043a\u0443\u0431\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V = S_{\u043e\u0441\u043d}*h\\)<\/li><li>\\(S =2S_{\u043e\u0441\u043d}+S_{\u0431\u043e\u043a}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 \\(S_{\u043e\u0441\u043d}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \\(h\\) \u2014 \u0432\u044b\u0441\u043e\u0442\u0430, \\(S_{\u0431\u043e\u043a}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V = abc\\)<\/li><li>\\(S = 2ab+2ac+2bc\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>a<\/em>, <em>b<\/em> \u0438 <em>c<\/em> \u2014 \u0434\u043b\u0438\u043d\u044b \u0440\u0435\u0431\u0435\u0440 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u0438\u0437\u043c\u0430:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V = S_{\u043e\u0441\u043d}*h\\)<\/li><li>\\(S =2S_{\u043e\u0441\u043d}+S_{\u0431\u043e\u043a}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 \\(S_{\u043e\u0441\u043d}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \\(h\\) \u2014 \u0432\u044b\u0441\u043e\u0442\u0430, \\(S_{\u0431\u043e\u043a}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0438\u0440\u0430\u043c\u0438\u0434\u0430:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V =\\frac{1}{3}S_{\u043e\u0441\u043d}*h\\)<\/li><li>\\(S =S_{\u043e\u0441\u043d}+S_{\u0431\u043e\u043a}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 \\(S_{\u043e\u0441\u043d}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \\(h\\) \u2014 \u0432\u044b\u0441\u043e\u0442\u0430, \\(S_{\u0431\u043e\u043a}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0426\u0438\u043b\u0438\u043d\u0434\u0440:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V =\\pi R^2h\u00a0\\)<\/li><li>\\(S =2S_{\u043e\u0441\u043d}+S_{\u0431\u043e\u043a}=2\\pi R^2+2\\pi Rh\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>R<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430,\u00a0\\(S_{\u043e\u0441\u043d}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439, \\(S_{\u0431\u043e\u043a}\\) \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438, \\(\\pi\\) \u2014 \u0447\u0438\u0441\u043b\u043e \u043f\u0438, \u0440\u0430\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 3,14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041a\u043e\u043d\u0443\u0441:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V =\\frac{1}{3}S_{\u043e\u0441\u043d}*h\\)<\/li><li>\\(S =2S_{\u043e\u0441\u043d}+S_{\u0431\u043e\u043a}=\\pi R^2+\\pi RL\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 \\(S_{\u043e\u0441\u043d} \u2014 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, <em>h<\/em> \u2014 \u0432\u044b\u0441\u043e\u0442\u0430, <em>R<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, <em>L<\/em> \u2014 \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0430\u044f, \\(\\pi\\) \u2014 \u0447\u0438\u0441\u043b\u043e \u043f\u0438, \u0440\u0430\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 3,14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0428\u0430\u0440:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(V =\\frac{4}{3}\\pi R^3\\)<\/li><li>\\(S =4\\pi R^2\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 <em>R<\/em> \u2014 \u0440\u0430\u0434\u0438\u0443\u0441, \\(\\pi\\) \u2014 \u0447\u0438\u0441\u043b\u043e \u043f\u0438, \u0440\u0430\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 3,14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0443\u043f\u0435\u0440, \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c, \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u043c \u043a \u043c\u0435\u0442\u043e\u0434\u0443 \u043e\u0431\u044a\u0435\u043c\u043e\u0432.<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041c\u0435\u0442\u043e\u0434 \u043e\u0431\u044a\u0435\u043c\u043e\u0432<\/strong> \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u043c \u043e\u0431\u044a\u0435\u043c \u043a\u0430\u043a\u043e\u0439-\u043d\u0438\u0431\u0443\u0434\u044c \u0444\u0438\u0433\u0443\u0440\u044b \u0434\u0432\u0443\u043c\u044f \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0443\u044e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0427\u0442\u043e\u0431\u044b \u043b\u0443\u0447\u0448\u0435 \u043f\u043e\u043d\u044f\u0442\u044c \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u043c\u0435\u0442\u043e\u0434\u0430 \u043e\u0431\u044a\u0435\u043c\u043e\u0432, \u0440\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u0447\u0443.&nbsp;<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430<strong> \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0432 \u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u211614. \u041c\u044b \u0440\u0435\u0448\u0438\u043c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0443\u043d\u043a\u0442 \u0431.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0412 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435 SABC \u0441 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c ABC \u0431\u043e\u043a\u043e\u0432\u043e\u0435 \u0440\u0435\u0431\u0440\u043e \u0440\u0430\u0432\u043d\u043e 20, \u0430 \u0441\u0442\u043e\u0440\u043e\u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u0430\u202f24.<\/em><br><em>\u0430) \u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e \u0432\u044b\u0441\u043e\u0442\u044b \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u044b, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0435 \u0438\u0437 \u0432\u0435\u0440\u0448\u0438\u043d A \u0438 S, \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/em><br><em>\u0431) \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0432\u0435\u0440\u0448\u0438\u043d\u044b A \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 SBC.<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/11-1024x1024.jpg\" alt=\"\" class=\"wp-image-36924\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/11-1024x1024.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/11-300x300.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/11-150x150.jpg 150w, \/library\/wp-content\/uploads\/2024\/03\/11-768x768.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/11.jpg 1188w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u0431)<em>SO<\/em>\u202f\u202f\u2014 \u0432\u044b\u0441\u043e\u0442\u0430 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u044b. \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u044d\u0442\u0443 \u0432\u044b\u0441\u043e\u0442\u0443, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u044b <em>AS <\/em>\u0438 <em>OA<\/em>. <em>AS <\/em>\u0437\u043d\u0430\u0435\u043c \u043f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0437\u0430\u0434\u0430\u0447\u0438, \u044d\u0442\u043e\u0442 \u043e\u0442\u0440\u0435\u0437\u043e\u043a \u0440\u0430\u0432\u0435\u043d 20. \u041d\u0430\u0439\u0434\u0435\u043c <em>OA<\/em>, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043e\u0442 \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u0434\u043e \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0432\u044b\u0441\u043e\u0442 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0447\u0435\u0440\u0435\u0437 \u0441\u0442\u043e\u0440\u043e\u043d\u0443 \u0438 \u0443\u0433\u043e\u043b \u0432 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0435 <em>ABC<\/em>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/12-1024x1024.jpg\" alt=\"\" class=\"wp-image-36925\" width=\"256\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/12-1024x1024.jpg 1024w, \/library\/wp-content\/uploads\/2024\/03\/12-300x300.jpg 300w, \/library\/wp-content\/uploads\/2024\/03\/12-150x150.jpg 150w, \/library\/wp-content\/uploads\/2024\/03\/12-768x768.jpg 768w, \/library\/wp-content\/uploads\/2024\/03\/12.jpg 1188w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\\(AO =BC*|ctg(A)|\\)<br><br><em>BC <\/em>\u2013 \u0441\u0442\u043e\u0440\u043e\u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \u0440\u0430\u0432\u043d\u0430\u044f 12, \u0430 \u0443\u0433\u043e\u043b <em>A <\/em>\u0440\u0430\u0432\u0435\u043d 60\u00b0, \u0442\u0430\u043a \u043a\u0430\u043a \u0432 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a.\u00a0<br><br>\\(AO =24*\\frac{\\sqrt{3}}{3}=8\\sqrt{3}\\)<br><br>\u041d\u0430\u0439\u0434\u0435\u043c <em>SO <\/em>\u043f\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430:<br><br>\\(SO =\\sqrt{AS^2-AO^2}=\\sqrt{400-192}=\\sqrt{208}=4\\sqrt{13}\\)<br><br>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043e\u0431\u044a\u0435\u043c\u0430 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u044b:\u00a0<br><br>\\(V =\\frac{1}{3}S_{\u043e\u0441\u043d}*h\\)<br><br>\u041d\u0430\u0439\u0434\u0435\u043c \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \u043f\u043e \u0441\u043e\u0432\u043c\u0435\u0441\u0442\u0438\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0433\u043e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430:<br><br>\\(S_{\u043e\u0441\u043d}=\\frac{a^2\\sqrt{3}}{4}\\)<br>\\(S_{\u043e\u0441\u043d}=\\frac{24^2\\sqrt{3}}{4}=144\\sqrt{3}\\)<br><br>\u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0439\u0434\u0435\u043c \u043e\u0431\u044a\u0435\u043c:<br><br>\\(V =\\frac{1}{3}*144\\sqrt{3}*4\\sqrt{13}=192\\sqrt{39}\\)<br><br>\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u043e\u0431\u044a\u0435\u043c\u043e\u0432. \u041c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u043e\u0431\u044a\u0435\u043c \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u044b <em>SABC<\/em> \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0438 \u0434\u0440\u0443\u0433\u0438\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u043c:<br><br>\\(V =\\frac{1}{3}S_{BSC}*AH\\)<br><br><em>AH <\/em>\u2014 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 <em>A <\/em>\u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 <em>BSC<\/em>, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438. \u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \\(S_{BSC}\\). \u041d\u0430\u0439\u0434\u0435\u043c \u0432\u044b\u0441\u043e\u0442\u0443 <em>SM <\/em>\u043f\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430:<br><br>\\(SM =\\sqrt{SB^2-BM^2}=\\sqrt{400-144}=\\sqrt{256}=16\\)<br><br>\u041f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 <em>SBC <\/em>\u0440\u0430\u0432\u043d\u0430:<br><br>\\(S_{SBC}=\\frac{1}{2}SM*BC=\\frac{1}{2}*16*24=192\\)<br><br>\u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0439\u0442\u0438 <em>AH<\/em>:<br><br>\\(V =\\frac{1}{3}S_{BSC}*AH\\)<br>\\(AH =\\frac{3V}{S_{BSC}}=\\frac{3*192\\sqrt{39}}{192}=3\\sqrt{39}\\)<br><br><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> \\(3\\sqrt{39}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043b\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043e\u0431\u044a\u0435\u043c\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u044b, \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u0440\u0430\u0437\u043d\u044b\u0445 \u0432\u044b\u0441\u043e\u0442 \u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439, \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0447\u0435\u0433\u043e \u0443 \u043d\u0430\u0441 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c \u043d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u041f\u043e \u0442\u0430\u043a\u043e\u0439 \u0436\u0435 \u043b\u043e\u0433\u0438\u043a\u0435 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0438 \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043a\u0440\u0435\u0449\u0438\u0432\u0430\u044e\u0449\u0438\u043c\u0438\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c\u0438.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0410 \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430?<\/strong><br><br>\u0427\u0435\u0442\u044b\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0435, \u043a\u043e\u043d\u0435\u0447\u043d\u043e. \u0424\u0438\u0437\u0438\u043a\u0438 \u0432\u044b\u0434\u0435\u043b\u044f\u044e\u0442 \u0432\u0440\u0435\u043c\u044f \u043a\u0430\u043a \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0435 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0435, \u0438 \u0442\u0430\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e-\u0432\u0440\u0435\u043c\u044f. \u041d\u0443 \u0430 \u043a\u0430\u043a \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0441\u0435\u0431\u0435 \u0447\u0435\u0442\u044b\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0435 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0435 \u2014 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435, \u0430 \u043d\u0435 \u0432\u0440\u0435\u043c\u044f?<br><br>\u041d\u0438\u043a\u0430\u043a. \u041a\u0430\u043a \u041c\u0430\u0440\u0438\u043e \u0438 \u041f\u0430\u043a\u043c\u0430\u043d, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u0432 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435, \u043d\u0435 \u0441\u043c\u043e\u0433\u043b\u0438 \u0431\u044b \u0441\u0435\u0431\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0442\u0440\u0435\u0442\u044c\u0435 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0435 \u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0438\u0433\u0440\u043e\u043a\u0430, \u0442\u0430\u043a \u0438 \u043c\u044b \u043d\u0435 \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0435.\u00a0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0438 \u043e\u0431\u044a\u0435\u043c\u043e\u0432. \u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0443\u0437\u043d\u0430\u0435\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 <a href=\"https:\/\/umschool.net\/library\/matematika\/vvedenie-v-zadachi-s-parametrom-reshenie-uravnenij-s-parametrom\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438<\/a>.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0424\u0430\u043a\u0442\u0447\u0435\u043a<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440<\/strong> \u2014 \u0434\u043b\u0438\u043d\u0430 \u0433\u0440\u0430\u043d\u0438\u0446\u044b \u0444\u0438\u0433\u0443\u0440\u044b.<\/li><li><strong>\u041f\u043b\u043e\u0449\u0430\u0434\u044c<\/strong> \u2014 \u043c\u0435\u0440\u0430 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u0444\u0438\u0433\u0443\u0440\u0430.<\/li><li><strong>\u041e\u0431\u044a\u0435\u043c <\/strong>\u2014 \u043c\u0435\u0440\u0430 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u0435\u043b\u043e.<\/li><li><strong>\u041c\u0435\u0442\u043e\u0434\u044b \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0438 \u043e\u0431\u044a\u0435\u043c\u043e\u0432<\/strong> \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u0438\u043b\u0438 \u043e\u0431\u044a\u0435\u043c\u0430 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438.&nbsp;<\/li><li>\u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0435\u0442\u043e\u0434\u0430 \u043e\u0431\u044a\u0435\u043c\u043e\u0432 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043a\u0440\u0435\u0449\u0438\u0432\u0430\u044e\u0449\u0438\u043c\u0438\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c\u0438 \u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e.<\/li><\/ul>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u041f\u0440\u043e\u0432\u0435\u0440\u044c \u0441\u0435\u0431\u044f<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 1.<\/strong><br>\u041a\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u0435\u0440\u0430 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u0435\u043b\u043e?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440<\/li><li>\u041f\u043b\u043e\u0449\u0430\u0434\u044c<\/li><li>\u041c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439<\/li><li>\u041e\u0431\u044a\u0435\u043c<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u0412 \u043a\u0430\u043a\u043e\u043c \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u0434\u0430\u043d\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u041d\u0415 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(S =\\frac{1}{2}ah\\)<\/li><li>\\(S =\\sqrt{p(p-a)(p-b)(p-c)}\\)<\/li><li>\\(S =\\frac{1}{2}d_1d_2\\)<\/li><li>\\(S = pr\\)<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u0412 \u0447\u0435\u043c \u0438\u0437\u043c\u0435\u0440\u044f\u044e\u0442 \u043e\u0431\u044a\u0435\u043c?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u0412 \u0441\u0430\u043d\u0442\u0438\u043c\u0435\u0442\u0440\u0430\u0445<\/li><li>\u0412 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0441\u0430\u043d\u0442\u0438\u043c\u0435\u0442\u0440\u0430\u0445<\/li><li>\u0412 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0430\u043d\u0442\u0438\u043c\u0435\u0442\u0440\u0430\u0445<\/li><li>\u0412 \u041d\u044c\u044e\u0442\u043e\u043d\u0430\u0445<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><br>\u041e\u0431\u044a\u0435\u043c \u043a\u0430\u043a\u043e\u0433\u043e \u0442\u0435\u043b\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \\(V =\\frac{1}{3}S_{\u043e\u0441\u043d}*h\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0438\u0440\u0430\u043c\u0438\u0434\u044b<\/li><li>\u041f\u0440\u0438\u0437\u043c\u044b<\/li><li>\u0428\u0430\u0440\u0430<\/li><li>\u041a\u0443\u0431\u0430<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442\u044b<\/strong>: <strong>1. \u2014 <\/strong>4;<strong> 2. \u2014 <\/strong>3;<strong> 3. \u2014 <\/strong>3;<strong> 4. \u2014 <\/strong>1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u041a\u0430\u043a \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043b\u0438\u043d\u0435\u0439\u043a\u0438 \u0438 \u0446\u0438\u0440\u043a\u0443\u043b\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438?&nbsp; \u041f\u043e\u0447\u0435\u043c\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0438 \u043e\u0431\u044a\u0435\u043c \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0431\u0443\u043a\u0432\u0430\u043c\u0438 P, S \u0438 V? \u0410 \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430? \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u043b\u0438\u0441\u044c \u043d\u0430\u043c \u043d\u0430 \u043f\u0440\u043e\u0442\u044f\u0436\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0432 \u0448\u043a\u043e\u043b\u0435. \u0414\u0430 \u0438 \u0432 \u0436\u0438\u0437\u043d\u0438 \u043e\u043d\u0438 \u043d\u0430\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f, \u0432\u0435\u0434\u044c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":36898,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[22],"tags":[],"class_list":["post-36897","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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\u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u041a\u0430\u043a \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043b\u0438\u043d\u0435\u0439\u043a\u0438 \u0438 \u0446\u0438\u0440\u043a\u0443\u043b\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438?&nbsp; \u041f\u043e\u0447\u0435\u043c\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0438 \u043e\u0431\u044a\u0435\u043c \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0431\u0443\u043a\u0432\u0430\u043c\u0438 P, S \u0438 V? \u0410 \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430? \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u043b\u0438\u0441\u044c \u043d\u0430\u043c \u043d\u0430 \u043f\u0440\u043e\u0442\u044f\u0436\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0432 \u0448\u043a\u043e\u043b\u0435. \u0414\u0430 \u0438 \u0432 \u0436\u0438\u0437\u043d\u0438 \u043e\u043d\u0438 \u043d\u0430\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f, \u0432\u0435\u0434\u044c [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/umschool.net\/library\/matematika\/perimetr-ploshhad-i-obem\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\" \/>\n<meta property=\"article:published_time\" 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