{"id":445,"date":"2022-04-12T10:36:32","date_gmt":"2022-04-12T10:36:32","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=445"},"modified":"2025-11-10T06:01:23","modified_gmt":"2025-11-10T06:01:23","slug":"w-3-area-of-triangles","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/w-3-area-of-triangles\/","title":{"rendered":"W.3 Area of triangles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Area of triangles<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG2-oDVnuw\/UGu_XLWm3K2VWYUOMvbtkQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG2-oDVnuw&#x2F;UGu_XLWm3K2VWYUOMvbtkQ&#x2F;watch?utm_content=DAG2-oDVnuw&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-primary-color has-text-color has-link-color wp-elements-48d81a8e0c3c16ad27b7d60b817bdf34\">\ud83c\udf1f <strong>Area of Triangles<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>What is Area?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>area<\/strong> of a shape is the <strong>amount of surface<\/strong> it covers.<\/li>\n\n\n\n<li>It is measured in <strong>square units<\/strong> (like cm\u00b2, m\u00b2, etc.).<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd3a <strong>Formula for the Area of a Triangle<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center\"><strong>Area=1\/2\u00d7base\u00d7height<\/strong><\/p>\n\n\n\n<p>\u2705 <strong>Base (b):<\/strong> The bottom side of the triangle.<\/p>\n\n\n\n<p>\u2705 <strong>Height (h):<\/strong> The perpendicular distance from the base to the opposite vertex.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udcd8 <strong>Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example 1:<\/strong><\/p>\n\n\n\n<p>If base = 10 cm and height = 8 cm<\/p>\n\n\n\n<p class=\"has-text-align-center\"> Area=1\/2\u00d710\u00d78=40&nbsp;cm<sup>2<\/sup><\/p>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<p>If base = 12 m and height = 5 m <\/p>\n\n\n\n<p class=\"has-text-align-center\">Area=1\/2\u00d712\u00d75=30&nbsp;m<sup>2<\/sup><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\u2728 <strong>Area of Special Triangles<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>a) Equilateral Triangle<\/strong><\/p>\n\n\n\n<p>All sides are equal. <\/p>\n\n\n\n<p class=\"has-text-align-center\">Area=\u221a3\/4\u00d7side<sup>2<\/sup><\/p>\n\n\n\n<p><strong>b) Isosceles Triangle<\/strong><\/p>\n\n\n\n<p>Two sides are equal. Use base and height (found using Pythagoras theorem if needed).<\/p>\n\n\n\n<p><strong>c) Right-Angled Triangle<\/strong><\/p>\n\n\n\n<p>The two shorter sides are base and height. <\/p>\n\n\n\n<p class=\"has-text-align-center\">Area=1\/2\u00d7(product&nbsp;of&nbsp;the&nbsp;two&nbsp;shorter&nbsp;sides)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udccf <strong>Units of Area<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Measurement<\/th><th>Unit of Area<\/th><\/tr><\/thead><tbody><tr><td>centimetres (cm)<\/td><td>square centimetres (cm\u00b2)<\/td><\/tr><tr><td>metres (m)<\/td><td>square metres (m\u00b2)<\/td><\/tr><tr><td>kilometres (km)<\/td><td>square kilometres (km\u00b2)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83e\uddee <strong>Area Using Heron\u2019s Formula<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>If the triangle\u2019s sides are <strong>a, b, c<\/strong> and height is not known:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> s=(a+b+c)\/2<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u200b Area=\u221as(s\u2212a)(s\u2212b)(s\u2212c)<\/p>\n\n\n\n<p>\ud83d\udc49 Useful when only the lengths of the sides are given.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udca1 <strong>Important Points<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2b50 Base and height must be <strong>perpendicular<\/strong> to each other.<\/li>\n\n\n\n<li>\u2b50 Area is <strong>always positive<\/strong>.<\/li>\n\n\n\n<li>\u2b50 Always write the <strong>unit<\/strong> after the answer.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83e\udde0 <strong>Quick Tip<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To remember the basic formula:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u201cHalf of base times height \u2014 gives area just right!\u201d \ud83d\ude04<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#acf4cf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u27a1\ufe0f <strong>What&nbsp;is the&nbsp;area?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2.png\" alt=\"\" class=\"wp-image-5261\" style=\"aspect-ratio:1;width:289px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____ What&nbsp;is the&nbsp;area?<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the base and height of the&nbsp;triangle.<\/p>\n\n\n\n<p>base:&nbsp;9&nbsp;m<\/p>\n\n\n\n<p>height:&nbsp;8&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;these numbers in the&nbsp;formula.<\/p>\n\n\n\n<p>area = 1\/2 . base . height<\/p>\n\n\n\n<p>= 1\/2 . 9 . 2<\/p>\n\n\n\n<p>= 36<\/p>\n\n\n\n<p>Now&nbsp;find the units. The lengths are measured in metres, so the area is measured in square&nbsp;metres.<\/p>\n\n\n\n<p>The&nbsp;area is&nbsp;36&nbsp;square&nbsp;metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#9aacf9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u27a1\ufe0f <strong>What&nbsp;is the area of the shaded&nbsp;region?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-2.png\" alt=\"\" class=\"wp-image-5262\" style=\"aspect-ratio:1;width:289px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-2.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-2-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-2-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-2-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____ &nbsp;square&nbsp;metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the base and height of the&nbsp;triangle.<\/p>\n\n\n\n<p>base:&nbsp;3&nbsp;m<\/p>\n\n\n\n<p>height:&nbsp;4&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;these numbers in the&nbsp;formula.<\/p>\n\n\n\n<p>area = 1\/2 . base . height<\/p>\n\n\n\n<p>= 1\/2 . 3 . 4<\/p>\n\n\n\n<p>= 6<\/p>\n\n\n\n<p>Now&nbsp;find the units. The lengths are measured in metres, so the area is measured in square&nbsp;metres.<\/p>\n\n\n\n<p>The&nbsp;area is&nbsp;6&nbsp;square&nbsp;metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#f0b7fe\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\u27a1\ufe0f What&nbsp;is the area of the shaded&nbsp;region?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-5-3.png\" alt=\"\" class=\"wp-image-5263\" style=\"aspect-ratio:1;width:283px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-5-3.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-5-3-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-5-3-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-5-3-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>____&nbsp;square&nbsp;millimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the base and height of the&nbsp;triangle.<\/p>\n\n\n\n<p>base:&nbsp;6&nbsp;mm<\/p>\n\n\n\n<p>height:&nbsp;6&nbsp;mm<\/p>\n\n\n\n<p>Use&nbsp;these numbers in the&nbsp;formula.<\/p>\n\n\n\n<p>area 1\/2 . base . height<\/p>\n\n\n\n<p>= 1\/2 . 6 . 6<\/p>\n\n\n\n<p>= 18<\/p>\n\n\n\n<p>Now&nbsp;find the units. The lengths are measured in millimetres, so the area is measured in square&nbsp;millimetres.<\/p>\n\n\n\n<p>The&nbsp;area is&nbsp;18&nbsp;square&nbsp;millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/101653\/328\/279\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-127.png\" alt=\"\" class=\"wp-image-6878\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-127.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-127-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-127-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-127-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/101653\/694\/453\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-129.png\" alt=\"\" class=\"wp-image-6879\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-129.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-129-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-129-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-129-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Area of triangles Design by Delta publications Key Notes : \ud83c\udf1f Area of Triangles \ud83d\udd39 What is Area? \ud83d\udd3a Formula for the Area of a Triangle Area=1\/2\u00d7base\u00d7height \u2705 Base (b): The bottom side of the triangle. \u2705 Height (h): The perpendicular distance from the base to the opposite vertex. \ud83d\udcd8 Examples Example 1: If base<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/w-3-area-of-triangles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.3 Area of triangles&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-445","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=445"}],"version-history":[{"count":23,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445\/revisions"}],"predecessor-version":[{"id":17553,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445\/revisions\/17553"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}