{"id":459,"date":"2022-04-12T10:38:39","date_gmt":"2022-04-12T10:38:39","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=459"},"modified":"2025-11-10T09:21:15","modified_gmt":"2025-11-10T09:21:15","slug":"w-10-area-between-two-shapes","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/w-10-area-between-two-shapes\/","title":{"rendered":"W.10 Area between two shapes"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Area between two shapes<\/strong><\/h2>\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<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Introduction<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Sometimes we need to find the area covered <strong>between two shapes<\/strong>.<\/p>\n\n\n\n<p>This usually happens when one shape is <strong>inside another<\/strong> (like a circle inside a square, or a rectangle inside another rectangle).<\/p>\n\n\n\n<p>The area between two shapes = <strong>Area of the larger shape \u2013 Area of the smaller shape<\/strong>.<\/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><strong><strong>Formula<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Area&nbsp;between&nbsp;two&nbsp;shapes=Area&nbsp;of&nbsp;Outer&nbsp;Shape\u2212Area&nbsp;of&nbsp;Inner&nbsp;Shape<\/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><strong><strong><strong>Steps to Solve<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify the <strong>outer shape<\/strong> and the <strong>inner shape<\/strong>.<\/li>\n\n\n\n<li>Find the <strong>area of the outer shape<\/strong> using the correct formula.<\/li>\n\n\n\n<li>Find the <strong>area of the inner shape<\/strong> using the correct formula.<\/li>\n\n\n\n<li>Subtract:\n<ul class=\"wp-block-list\">\n<li>            Required&nbsp;Area=Outer&nbsp;Area\u2212Inner&nbsp;Area<\/li>\n<\/ul>\n<\/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><strong><strong><strong><strong>Examples<\/strong><\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example 1: Rectangle with a smaller rectangle cut out<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Outer rectangle: length = 12 cm, breadth = 8 cm<\/li>\n\n\n\n<li>Inner rectangle: length = 6 cm, breadth = 4 cm<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\">Outer&nbsp;Area=12\u00d78=96\u2009cm<sup>2<\/sup><\/p>\n\n\n\n<p class=\"has-normal-font-size\"> Inner&nbsp;Area=6\u00d74=24\u2009cm<sup>2<\/sup><\/p>\n\n\n\n<p> Area between&nbsp;two&nbsp;rectangles=96\u221224=72\u2009cm<sup>2<\/sup><\/p>\n\n\n\n<p><strong>Example 2: Square with a circle inside<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Square side = 14 cm<\/li>\n\n\n\n<li>Circle radius = 7 cm<\/li>\n<\/ul>\n\n\n\n<p>Area&nbsp;of&nbsp;square=14\u00d714=196\u2009cm<sup>2<\/sup><\/p>\n\n\n\n<p>Area&nbsp;of&nbsp;circle=\u03c0r<sup>2<\/sup>=22\/7\u00d77\u00d77=154\u2009cm<sup>2<\/sup> <\/p>\n\n\n\n<p>Area&nbsp;between&nbsp;square&nbsp;and&nbsp;circle=196\u2212154=42\u2009cm<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><strong><strong><strong><strong><strong> Common Shapes and Their Areas<\/strong><\/strong><\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rectangle \u2192 l\u00d7b <\/li>\n\n\n\n<li>Square \u2192 a<sup>2<\/sup><\/li>\n\n\n\n<li>Triangle \u2192 1\/2\u00d7base\u00d7height<\/li>\n\n\n\n<li>Circle \u2192 \u03c0r<sup>2<\/sup><\/li>\n\n\n\n<li>Parallelogram \u2192 base\u00d7height<\/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><strong>Key Points<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always subtract <strong>smaller shape area<\/strong> from <strong>larger shape area<\/strong>.<\/li>\n\n\n\n<li>Be careful with units (cm\u00b2, m\u00b2, etc.).<\/li>\n\n\n\n<li>Sometimes inner shapes may be circles, rectangles, or triangles.<\/li>\n\n\n\n<li>This concept is often used in <strong>real life<\/strong>, e.g., finding garden paths, borders, or rings.<\/li>\n<\/ul>\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-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-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#e6d3f9\"><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\">\u25b6\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-7-5.png\" alt=\"\" class=\"wp-image-5300\" style=\"aspect-ratio:1;width:424px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-5.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-5-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-5-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-5-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Write&nbsp;your answer as a whole number or a decimal rounded to the nearest&nbsp;hundredth.&nbsp;&nbsp;<\/p>\n\n\n\n<p>_______ square metres<\/p>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;find the area of the shaded region, subtract the area of the inner shape from the area of the outer shape. Start by finding the area of the inner&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the base and height of the inner&nbsp;triangle.<\/p>\n\n\n\n<p>base:&nbsp;8&nbsp;m<\/p>\n\n\n\n<p>height:&nbsp;12&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;these numbers in the&nbsp;formula.<\/p>\n\n\n\n<p>inner&nbsp;area = 1\/2 . base . height<\/p>\n\n\n\n<p>= 1\/2 . 8 . 12<\/p>\n\n\n\n<p>= 48<\/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 of the inner triangle is&nbsp;48&nbsp;square&nbsp;metres.<\/p>\n\n\n\n<p>Next,&nbsp;find the area of the outer&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the base and height of the outer&nbsp;triangle.<\/p>\n\n\n\n<p>base:&nbsp;13&nbsp;m<\/p>\n\n\n\n<p>height:&nbsp;17&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;these numbers in the&nbsp;formula.<\/p>\n\n\n\n<p>outer&nbsp;area = 1\/2 base . height<\/p>\n\n\n\n<p>= 1\/2 . 13 . 17<\/p>\n\n\n\n<p>= 110.5<\/p>\n\n\n\n<p>As&nbsp;with the inner triangle, the lengths of the outer triangle are measured in metres. So, the area is measured in square&nbsp;metres.<\/p>\n\n\n\n<p>The&nbsp;area of the outer triangle is&nbsp;110.5&nbsp;square&nbsp;metres.<\/p>\n\n\n\n<p>Finally,&nbsp;subtract the inner area from the outer area to find the area of the shaded&nbsp;region.<\/p>\n\n\n\n<p>shaded&nbsp;area = 110.5 \u2013 48<\/p>\n\n\n\n<p>= 62.5<\/p>\n\n\n\n<p>The area of the shaded region is 62.5 square 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:#f9d4d4\"><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\">\u25b6\ufe0f <strong>What&nbsp;is the area of the shaded&nbsp;region?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-2.png\" alt=\"\" class=\"wp-image-5303\" style=\"aspect-ratio:1;width:350px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-2.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-2-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-2-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-2-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____ &nbsp;square&nbsp;centimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;find the area of the shaded region, subtract the area of the inner shape from the area of the outer shape. Start by finding the area of the inner&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the side length of the inner&nbsp;square.<\/p>\n\n\n\n<p>side:&nbsp;10&nbsp;cm<\/p>\n\n\n\n<p>Use&nbsp;this number in the&nbsp;formula.<\/p>\n\n\n\n<p>inner&nbsp;area=side<\/p>\n\n\n\n<p>side = 10 . 10<\/p>\n\n\n\n<p>=100<\/p>\n\n\n\n<p>Now&nbsp;find the units. The lengths are measured in centimetres, so the area is measured in square&nbsp;centimetres.<\/p>\n\n\n\n<p>The&nbsp;area of the inner square is&nbsp;100&nbsp;square&nbsp;centimetres.<\/p>\n\n\n\n<p>Next,&nbsp;find the area of the outer&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the side length of the outer&nbsp;square.<\/p>\n\n\n\n<p>side:&nbsp;19&nbsp;cm<\/p>\n\n\n\n<p>Use&nbsp;this number in the&nbsp;formula.<\/p>\n\n\n\n<p>outer&nbsp;area=side . side<\/p>\n\n\n\n<p>=19 . 19<\/p>\n\n\n\n<p>=361<\/p>\n\n\n\n<p>As&nbsp;with the inner square, the lengths of the outer square are measured in centimetres. So, the area is measured in square&nbsp;centimetres.<\/p>\n\n\n\n<p>The&nbsp;area of the outer square is&nbsp;361&nbsp;square&nbsp;centimetres.<\/p>\n\n\n\n<p>Finally,&nbsp;subtract the inner area from the outer area to find the area of the shaded&nbsp;region.<\/p>\n\n\n\n<p>shaded&nbsp;area = 361 \u2013 100<\/p>\n\n\n\n<p>= 261<\/p>\n\n\n\n<p>The&nbsp;area of the shaded region is 261 square&nbsp;centimetres.<\/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:#f9eed4\"><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\">\u25b6\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-9-3.png\" alt=\"\" class=\"wp-image-5306\" style=\"aspect-ratio:1;width:398px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-9-3.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-9-3-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-9-3-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-9-3-400x400.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>To&nbsp;find the area of the shaded region, subtract the area of the inner shape from the area of the outer shape. Start by finding the area of the inner&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the side length of the inner&nbsp;square.<\/p>\n\n\n\n<p>side:&nbsp;6&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;this number in the&nbsp;formula.<\/p>\n\n\n\n<p>inner&nbsp;area = side . side<\/p>\n\n\n\n<p>= 6 . 6<\/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 of the inner square is&nbsp;36&nbsp;square&nbsp;metres.<\/p>\n\n\n\n<p>Next,&nbsp;find the area of the outer&nbsp;shape.<\/p>\n\n\n\n<p>Find&nbsp;the side length of the outer&nbsp;square.<\/p>\n\n\n\n<p>side:&nbsp;17&nbsp;m<\/p>\n\n\n\n<p>Use&nbsp;this number in the&nbsp;formula.<\/p>\n\n\n\n<p>outer&nbsp;area=side . side<\/p>\n\n\n\n<p>= 17 . 17<\/p>\n\n\n\n<p>= 289<\/p>\n\n\n\n<p>As&nbsp;with the inner square, the lengths of the outer square are measured in metres. So, the area is measured in square&nbsp;metres.<\/p>\n\n\n\n<p>The&nbsp;area of the outer square is&nbsp;289&nbsp;square&nbsp;metres.<\/p>\n\n\n\n<p>Finally,&nbsp;subtract the inner area from the outer area to find the area of the shaded&nbsp;region.<\/p>\n\n\n\n<p>shaded&nbsp;area = 289 \u2013 36<\/p>\n\n\n\n<p>= 253<\/p>\n\n\n\n<p>The&nbsp;area of the shaded region is 253 square&nbsp;metres.<\/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<\/div>\n<\/div>\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\/101666\/318\/944\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-134.png\" alt=\"\" class=\"wp-image-6899\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-134.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-134-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-134-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-134-400x400.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\/101667\/127\/582\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-136.png\" alt=\"\" class=\"wp-image-6900\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-136.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-136-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-136-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-136-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Area between two shapes Key Notes : Introduction Sometimes we need to find the area covered between two shapes. This usually happens when one shape is inside another (like a circle inside a square, or a rectangle inside another rectangle). The area between two shapes = Area of the larger shape \u2013 Area of the<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/w-10-area-between-two-shapes\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.10 Area between two shapes&#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-459","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/459","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=459"}],"version-history":[{"count":24,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/459\/revisions"}],"predecessor-version":[{"id":17575,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/459\/revisions\/17575"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}