{"id":1122,"date":"2020-07-08T03:22:02","date_gmt":"2020-07-07T19:22:02","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1122"},"modified":"2020-11-02T23:13:34","modified_gmt":"2020-11-02T15:13:34","slug":"area-and-volume","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/area-and-volume\/","title":{"rendered":"11. \u9762\u7a4d\u53ca\u9ad4\u7a4d (Area and Volume)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1122\" class=\"elementor elementor-1122\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0dbd626 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0dbd626\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-b5674ed\" data-id=\"b5674ed\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-90d0909 elementor-widget elementor-widget-text-editor\" data-id=\"90d0909\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5e73\u9762\u9762\u7a4d\u516c\u5f0f<\/h2><p>\u5176\u5be6\u4e2d\u4e00\u8981\u5b78\u5605\u5e73\u9762\u9762\u7a4d\u516c\u5f0f\u55ba\u5c0f\u5b78\u5605\u6642\u5019\u5df2\u7d93\u5b78\u5497\u3002<\/p><p style=\"padding-left: 40px;\">\\( \\begin{align}<br \/>\u6b63\u65b9\u5f62\u9762\u7a4d &amp; =\u3000\u908a\u9577 \\times \u908a\u9577 \\\\<br \/>\u9577\u65b9\u5f62\u9762\u7a4d &amp; =\u3000\u9577 \\times \u6ff6 \\\\<br \/>\u4e09\u89d2\u5f62\u9762\u7a4d &amp; = \\dfrac{\u5e95 \\times\u00a0 \u9ad8}{2} \\\\<br \/>\u5e73\u884c\u56db\u908a\u5f62\u9762\u7a4d &amp; =\u3000\u5e95 \\times \u9ad8 \\\\<br \/>\u68af\u5f62\u9762\u7a4d &amp; = \\dfrac{\u5169\u689d\u5e73\u884c\u908a\u7684\u548c}{2} = \\dfrac{\u4e0a\u5e95 + \u4e0b\u5e95}{2} \\\\<br \/>\\end{align} \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6fa1acb elementor-widget elementor-widget-text-editor\" data-id=\"6fa1acb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u9ad4\u7a4d\u516c\u5f0f<\/h2><p>\u4e2d\u4e00\u8981\u5b78\u5605\u9ad4\u7a4d\u516c\u5f0f\u90fd\u55ba\u5c0f\u5b78\u5605\u6642\u5019\u5df2\u7d93\u5b78\u5497\u3002<\/p><p style=\"padding-left: 40px;\">\\( \\begin{align}<br \/>\u6b63\u65b9\u9ad4\u9ad4\u7a4d\u00a0 &amp; =\u3000\u908a\u9577 \\times \u908a\u9577 \\times\u00a0 \u908a\u9577 \\\\<br \/>\u9577\u65b9\u9ad4\u9762\u7a4d &amp; =\u3000\u9577 \\times \u6ff6 \\times \u9ad8\u3000\\\\<br \/>\u67f1\u9ad4\u9ad4\u7a4d &amp; =\u3000\u6a6b\u5207\u9762\u9762\u7a4d \\times \u9ad8 \\\\<br \/>\u9310\u9ad4\u9ad4\u7a4d &amp; =\u3000\\dfrac{1}{3} \\times \u5e95\u9762\u7a4d \\times \u9ad8 \\\\<br \/>\\end{align} \\)<\/p><p>\u7559\u610f\u5176\u5be6\u6b63\u65b9\u9ad4\u540c\u9577\u65b9\u9ad4\u90fd\u4fc2\u67f1\u9ad4\u569f\u5605\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ac4c88a elementor-widget elementor-widget-text-editor\" data-id=\"ac4c88a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7c21\u55ae\u591a\u908a\u5f62\u7684\u9762\u7a4d (Area for Simple Polygon)<\/h2><ul><li>\u7576\u8981\u8a08\u7b97\u591a\u908a\u5f62\u5605\u9762\u7a4d\u6642\u5019\uff0c\u5176\u5be6\u53ef\u4ee5\u5148\u5c07\u591a\u908a\u5f62\u5206\u5272\u6210\u4e09\u89d2\u5f62\u3001\u9577\u65b9\u5f62\u3001\u5e73\u884c\u56db\u908a\u5f62\u6216\u68af\u5f62\u7b49\u7c21\u55ae\u5716\u5f62\u3002<ul><li>\u539f\u56e0\uff1a \u4e09\u89d2\u5f62\u3001\u9577\u65b9\u5f62\u7b49\u7c21\u55ae\u5716\u5f62\u7684\u500b\u5225\u9762\u7a4d\u53ef\u76f4\u63a5\u5229\u7528\u516c\u5f0f\u6c42\u5f97\uff0c\u800c\u6574\u500b\u591a\u908a\u5f62\u7684\u9762\u7a4d\u5c31\u53ef\u4ee5\u5229\u7528\u500b\u5225\u7c21\u55ae\u5716\u5f62\u9762\u7a4d\u7684\u548c\u6216\u5dee\u800c\u6c42\u5f97\u3002<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-159249e elementor-widget elementor-widget-text-editor\" data-id=\"159249e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u67f1\u9ad4<\/h2><p>\u6709\u95dc\u67f1\u9ad4\u5605\u516c\u5f0f\u6709\u4ee5\u4e0b3\u689d\uff1a<\/p><ul><li>\u67f1\u9ad4\u9ad4\u7a4d\u00a0 = \u6a6b\u5207\u9762\u9762\u7a4d \u00d7 \u9ad8 = \u5e95\u9762\u7a4d \u00d7 \u9ad8<\/li><li>\u67f1\u9ad4\u5074\u9762\u9762\u7a4d = \u6a6b\u5207\u9762\u5468\u754c \u00d7 \u9ad8 = \u5e95\u7684\u5468\u754c \u00d7 \u9ad8<\/li><li>\u67f1\u9ad4\u7e3d\u9762\u7a4d\u00a0 = \u5e95\u9762\u7a4d \uff0b \u9802\u9762\u7a4d \uff0b \u5074\u9762\u9762\u7a4d = \u5e95\u9762\u7a4d \u00d7 2 \uff0b \u5074\u9762\u9762\u7a4d<\/li><\/ul><p>\u5176\u5be6\u4e2d\u4e00\u65b0\u5b78\u5605\u5c31\u4fc2\u67f1\u9ad4\u5605\u5074\u9762\u9762\u7a4d\u3002\u689d\u516c\u5f0f\u5c31\u597d\u4f3c\u597d\u96e3\u7406\u89e3\u5481\uff0c\u4f46\u5927\u5bb6\u5176\u5be6\u53ea\u8981\u651e\u4e00\u5f35\u9577\u65b9\u5f62\u5605\u7d19\u569f\u5305\u4f4f\u500b\u5074\u9762, \u5c31\u61c9\u53ef\u4ee5\u7747\u5230\u9577\u65b9\u5f62\u7d19\u5605\u9577\u5ea6\u5176\u5be6\u5c31\u4fc2\u500b\u67f1\u9ad4\u500b\u5e95\u5605\u5468\u754c\u3002<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-1131 aligncenter\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_cylinderLateralArea.jpg\" alt=\"\u9577\u65b9\u5074\u9762\u9762\u7a4d\u516c\u5f0f\u89e3\u91cb\" width=\"519\" height=\"177\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_cylinderLateralArea.jpg 519w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_cylinderLateralArea-300x102.jpg 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/>\u56e0\u6b64\uff0c\u5074\u9762\u9762\u7a4d = \u9577\u65b9\u7d19\u9762\u7a4d = \u67f1\u9ad4\u5e95\u5468\u754c \u00d7 \u9ad8<\/p><p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-3c2996f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c2996f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4695dbc\" data-id=\"4695dbc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1502f21 elementor-widget elementor-widget-text-editor\" data-id=\"1502f21\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/estimation-in-measurements\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u91cf\u5ea6\u65b9\u9762\u7684\u4f30\u8a08<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-20aa386\" data-id=\"20aa386\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-860a6b1\" data-id=\"860a6b1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-92f3e69 elementor-widget elementor-widget-text-editor\" data-id=\"92f3e69\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-coordinates\/\">\u5750\u6a19\u7c21\u4ecb <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-791951b\" data-id=\"791951b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a36a128 elementor-widget elementor-widget-sidebar\" data-id=\"a36a128\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-2 > ul > li > a, .custom-menu-widget .ocean_custom_menu-2 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-2.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e00\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-2 left dropdown-hover\"><ul id=\"menu-form1mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-928\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-928\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/directed-numbers\/\" class=\"menu-link\">1. \u6709\u5411\u6578 (Directed Numbers)<\/a><\/li>\n<li  id=\"menu-item-929\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-929\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/algebraic-expressions-equations\/\" class=\"menu-link\">2. \u4ee3\u6578\u5f0f\u548c\u65b9\u7a0b\u5f0f (Algebraic Expressions &#038; Equations)<\/a><\/li>\n<li  id=\"menu-item-995\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-995\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/laws-of-integral-indices\/\" class=\"menu-link\">3. \u6307\u6578\u53ca\u9032\u5236 (Laws of integral indices)<\/a><\/li>\n<li  id=\"menu-item-1000\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1000\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/polynomials\/\" class=\"menu-link\">4. \u591a\u9805\u5f0f (Polynomials)<\/a><\/li>\n<li  id=\"menu-item-1043\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1043\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/using-percentages\/\" class=\"menu-link\">5. \u767e\u5206\u6cd5 (Using percentages)<\/a><\/li>\n<li  id=\"menu-item-1053\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1053\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/approximate-values-estimation\/\" class=\"menu-link\">6. \u8fd1\u4f3c\u503c\u8207\u4f30\u7b97 (Approximate values &#038; estimation)<\/a><\/li>\n<li  id=\"menu-item-1071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1071\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-geometry\/\" class=\"menu-link\">7. \u5e7e\u4f55\u7c21\u4ecb (Introduction to Geometry)<\/a><\/li>\n<li  id=\"menu-item-1093\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1093\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/symmetry-and-transformation\/\" class=\"menu-link\">8. \u5c0d\u7a31\u53ca\u8b8a\u63db (Symmetry and Transformation)<\/a><\/li>\n<li  id=\"menu-item-1109\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1109\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/congruence-and-similarity\/\" class=\"menu-link\">9. \u5168\u7b49\u53ca\u76f8\u4f3c (Congruence and Similarity)<\/a><\/li>\n<li  id=\"menu-item-1120\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1120\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/estimation-in-measurements\/\" class=\"menu-link\">10. \u91cf\u5ea6\u65b9\u9762\u7684\u4f30\u8a08 (Estimation in measurements)<\/a><\/li>\n<li  id=\"menu-item-1136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/area-and-volume\/\" class=\"menu-link\">11. \u9762\u7a4d\u53ca\u9ad4\u7a4d (Area and Volume)<\/a><\/li>\n<li  id=\"menu-item-1150\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1150\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-coordinates\/\" class=\"menu-link\">12.   \u5750\u6a19\u7c21\u4ecb (Introduction to Coordinates)<\/a><\/li>\n<li  id=\"menu-item-1164\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1164\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-statistics\/\" class=\"menu-link\">13.  \u7d71\u8a08\u7c21\u4ecb (Introduction to Statistics)<\/a><\/li>\n<li  id=\"menu-item-16138\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16138\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>11.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5e73\u9762\u9762\u7a4d\u516c\u5f0f \u5176\u5be6\u4e2d\u4e00\u8981\u5b78\u5605\u5e73\u9762\u9762\u7a4d\u516c\u5f0f\u55ba\u5c0f\u5b78\u5605\u6642\u5019\u5df2\u7d93\u5b78\u5497\u3002 ( begin{alig 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