{"id":226649,"date":"2025-06-05T12:27:57","date_gmt":"2025-06-05T12:27:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226649"},"modified":"2025-06-05T12:27:59","modified_gmt":"2025-06-05T12:27:59","slug":"find-the-perimeter-and-area-of-the-shaded-figure-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/find-the-perimeter-and-area-of-the-shaded-figure-below\/","title":{"rendered":"Find the perimeter and area of the shaded figure below"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Find the perimeter and area of the shaded figure below: Perimeter: 12 units Area: 8 square units<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-155.png\" alt=\"\" class=\"wp-image-226650\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The <strong>correct answer<\/strong> for the shaded figure in the image is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Area:<\/strong> 8 square units \u2705<\/li>\n\n\n\n<li><strong>Perimeter:<\/strong> <strong>18 units<\/strong> \u274c (not 12 units as shown in the image)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udccf Explanation<\/h3>\n\n\n\n<p>To determine the <strong>area<\/strong> and <strong>perimeter<\/strong> of the shaded rectangle, we must examine the figure closely.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2705 Area<\/h4>\n\n\n\n<p>Area is calculated using the formula for the area of a rectangle: Area=Length\u00d7Width\\text{Area} = \\text{Length} \\times \\text{Width}<\/p>\n\n\n\n<p>From the grid:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The shaded figure spans <strong>4 squares vertically<\/strong> (length).<\/li>\n\n\n\n<li>It spans <strong>2 squares horizontally<\/strong> (width).<\/li>\n<\/ul>\n\n\n\n<p>So, Area=4\u00d72=8&nbsp;square&nbsp;units\\text{Area} = 4 \\times 2 = 8 \\text{ square units}<\/p>\n\n\n\n<p>This confirms that the <strong>given area is correct<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u274c Perimeter<\/h4>\n\n\n\n<p>Perimeter is the total distance around the outside of the figure. For a rectangle: Perimeter=2\u00d7(Length+Width)\\text{Perimeter} = 2 \\times (\\text{Length} + \\text{Width})<\/p>\n\n\n\n<p>Using the same measurements:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Length = 4 units<\/li>\n\n\n\n<li>Width = 2 units<\/li>\n<\/ul>\n\n\n\n<p>Perimeter=2\u00d7(4+2)=2\u00d76=12&nbsp;units\\text{Perimeter} = 2 \\times (4 + 2) = 2 \\times 6 = 12 \\text{ units}<\/p>\n\n\n\n<p>Wait\u2014that suggests <strong>12 units<\/strong> is correct. But let\u2019s verify using the grid.<\/p>\n\n\n\n<p>Looking carefully at the shaded figure:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Height (vertical sides):<\/strong> 4 units (2 sides \u2192 4 + 4 = 8)<\/li>\n\n\n\n<li><strong>Width (horizontal sides):<\/strong> 1 unit (2 sides \u2192 1 + 1 = 2)<\/li>\n<\/ul>\n\n\n\n<p>There is an error in labeling. The rectangle is <strong>4 units high<\/strong> and <strong>1 unit wide<\/strong>, <strong>not<\/strong> 2 units wide. So the correct dimensions are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Length = 4 units<\/li>\n\n\n\n<li>Width = 1 unit<\/li>\n<\/ul>\n\n\n\n<p>Now recalculate: Area=4\u00d71=4&nbsp;square&nbsp;units\\text{Area} = 4 \\times 1 = 4 \\text{ square units} Perimeter=2\u00d7(4+1)=2\u00d75=10&nbsp;units\\text{Perimeter} = 2 \\times (4 + 1) = 2 \\times 5 = 10 \\text{ units}<\/p>\n\n\n\n<p>But <strong>based on actual counting of grid squares<\/strong>, the shaded figure is <strong>4 units high<\/strong> and <strong>2 units wide<\/strong>, making:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Area = 4 \u00d7 2 = 8 square units<\/strong><\/li>\n\n\n\n<li><strong>Perimeter = 2 \u00d7 (4 + 2) = 12 units<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So the <strong>original answer in the image is actually correct<\/strong>, and my initial correction was mistaken.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Area:<\/strong> 8 square units<\/li>\n\n\n\n<li><strong>Perimeter:<\/strong> 12 units<\/li>\n<\/ul>\n\n\n\n<p>The original solution is correct after all!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-230.jpeg\" alt=\"\" class=\"wp-image-226651\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the perimeter and area of the shaded figure below: Perimeter: 12 units Area: 8 square units The Correct Answer and Explanation is: The correct answer for the shaded figure in the image is: \ud83d\udccf Explanation To determine the area and perimeter of the shaded rectangle, we must examine the figure closely. \u2705 Area Area [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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