{"id":229340,"date":"2025-06-08T06:20:03","date_gmt":"2025-06-08T06:20:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229340"},"modified":"2025-06-08T06:20:05","modified_gmt":"2025-06-08T06:20:05","slug":"find-the-area-of-the-figure","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/find-the-area-of-the-figure\/","title":{"rendered":"Find the area of the figure."},"content":{"rendered":"\n

Find the area of the figure.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the area of the given figure<\/strong>, we need to break it into two simpler shapes:<\/p>\n\n\n\n

    \n
  1. A rectangle<\/strong> in the middle.<\/li>\n\n\n\n
  2. A circle<\/strong>, formed by combining the two semicircles on each end of the rectangle.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    \ud83d\udd39 Step 1: Area of the Rectangle<\/h3>\n\n\n\n

    The rectangle<\/strong> in the center has:<\/p>\n\n\n\n

      \n
    • Length = 12 ft<\/strong><\/li>\n\n\n\n
    • Width = 3 ft<\/strong><\/li>\n<\/ul>\n\n\n\n

      Area of rectangle=length\u00d7width=12\u00d73=36 ft2\\text{Area of rectangle} = \\text{length} \\times \\text{width} = 12 \\times 3 = 36 \\text{ ft}^2Area of rectangle=length\u00d7width=12\u00d73=36 ft2<\/p>\n\n\n\n

      \n\n\n\n

      \ud83d\udd39 Step 2: Area of the Circle<\/h3>\n\n\n\n

      There are two semicircles<\/strong> on each end of the rectangle. Together, they make one full circle<\/strong>.<\/p>\n\n\n\n

      From the image:<\/p>\n\n\n\n

        \n
      • Each semicircle has a radius of 3 ft<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Area of full circle=\u03c0r2=\u03c0(3)2=9\u03c0\u224828.27 ft2\\text{Area of full circle} = \\pi r^2 = \\pi (3)^2 = 9\\pi \\approx 28.27 \\text{ ft}^2Area of full circle=\u03c0r2=\u03c0(3)2=9\u03c0\u224828.27 ft2<\/p>\n\n\n\n

        \n\n\n\n

        \ud83d\udd39 Step 3: Total Area<\/h3>\n\n\n\n

        Now, add the area of the rectangle and the circle:Total Area=36+9\u03c0\u224836+28.27=64.27 ft2\\text{Total Area} = 36 + 9\\pi \\approx 36 + 28.27 = \\boxed{64.27 \\text{ ft}^2}Total Area=36+9\u03c0\u224836+28.27=64.27 ft2\u200b<\/p>\n\n\n\n

        \n\n\n\n

        \u2705 Final Answer: 64.27 square feet<\/strong><\/h3>\n\n\n\n
        \n\n\n\n

        \ud83d\udd0d Explanation<\/h3>\n\n\n\n

        The composite shape in the image combines a rectangle and two semicircles to form a more complex figure. To find the area accurately, we apply the strategy of breaking down the shape into simpler components<\/strong>.<\/p>\n\n\n\n

        The central rectangle is easy to calculate. From the image, its length runs horizontally and measures 12 feet. The height or width is 3 feet. By multiplying these two dimensions, we get the area of the rectangle as 12\u00d73=3612 \\times 3 = 3612\u00d73=36 square feet.<\/p>\n\n\n\n

        The curved ends are not full circles but two half circles<\/strong> attached on each side. Because the diameter of each semicircle is 6 feet (the same as the height of the full shape), the radius is half of that, or 3 feet. Adding both halves together forms a full circle with radius 3 feet. Using the circle area formula \u03c0r2\\pi r^2\u03c0r2, we substitute r=3r = 3r=3 to get \u03c0\u00d79=9\u03c0\u224828.27\\pi \\times 9 = 9\\pi \\approx 28.27\u03c0\u00d79=9\u03c0\u224828.27 square feet.<\/p>\n\n\n\n

        After calculating both parts\u2014the rectangle and the circle\u2014we add them together to find the full area of the shape: 36+28.27=64.2736 + 28.27 = 64.2736+28.27=64.27 square feet.<\/p>\n\n\n\n

        This process shows the importance of visual decomposition in geometry. Recognizing standard shapes (like rectangles and circles) within a compound figure simplifies the calculation and ensures precision.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Find the area of the figure. The Correct Answer and Explanation is: To find the area of the given figure, we need to break it into two simpler shapes: \ud83d\udd39 Step 1: Area of the Rectangle The rectangle in the center has: Area of rectangle=length\u00d7width=12\u00d73=36 ft2\\text{Area of rectangle} = \\text{length} \\times \\text{width} = 12 \\times 3 = 36 […]<\/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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-229340","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=229340"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229340\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}