{"id":79396,"date":"2021-03-29T12:33:19","date_gmt":"2021-03-29T07:03:19","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=79396"},"modified":"2022-04-01T10:27:15","modified_gmt":"2022-04-01T04:57:15","slug":"find-the-area-of-the-shaded-region","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/find-the-area-of-the-shaded-region\/","title":{"rendered":"Find the Area of the Shaded Region &#8211;  Simple and Easy Method"},"content":{"rendered":"<p>The area of the shaded region is the difference between two geometrical shapes which are combined together. By subtracting the area of the smaller geometrical shape from the area of the larger geometrical shape, we will get the area of the shaded region. Or subtract the area of the unshaded region from the area of the entire region that is also called an area of the shaded region.<\/p>\n<p>Area of the shaded region = Area of the large geometrical shape (entire region) \u2013 area of the small geometrical shape (shaded region).<\/p>\n<p>Do Refer:<\/p>\n<ul>\n<li><a href=\"https:\/\/ccssmathanswers.com\/area-of-a-square\/\">Area of a Square<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/areas-of-irregular-figures\/\">Areas of Irregular Figures<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/area-of-a-polygon\/\">Area of a Polygon<\/a><\/li>\n<\/ul>\n<h2>How to Find the Area of a Shaded Region?<\/h2>\n<p>Follow the below steps and know the process to find out the Area of the Shaded Region. We have given clear details along with the solved examples below.<\/p>\n<ul>\n<li>Firstly, find out the area of the large geometrical shape or outer region.<\/li>\n<li>Then, find the area of the small geometrical shape or inner region of the image.<\/li>\n<li>Finally, subtract an area of the small geometrical shape (entire region) from the large area of the small geometrical shape (shaded region).<\/li>\n<li>The resultant value is considered as the area of the shaded region.<\/li>\n<\/ul>\n<h3>Area of the Shaded Region Examples<\/h3>\n<p><strong>Problem 1.<\/strong><\/p>\n<p>A regular hexagon is inscribed in a circle with a radius of 21cm. Find out the area of the shaded region?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-79927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Regular-Hexagon-Inscribed-in-a-Circle-Shaded-Region.png\" alt=\"Regular Hexagon Inscribed in a Circle Shaded Region\" width=\"273\" height=\"256\" \/><\/p>\n<p><strong>Solution:<\/strong><br \/>\nAs per the given information,<br \/>\nHexagon is inscribed in a circle.<br \/>\nRadius of the circle = 21cm.<br \/>\nArea of the circle = A=\u03c0r\u00b2.<br \/>\nSubstituting the radius (r) value in the above equation, we will get<br \/>\nA = \u03c0(21)\u00b2.<br \/>\nA = 22 \/ 7(21 * 21).<br \/>\nA = 22(3*21).<br \/>\nA = 1386.<br \/>\nArea of the circle (A) = 1386 cm\u00b2.<br \/>\nArea of the hexagon = 3\u221a3\/ 2 r\u00b2.<br \/>\nSubstitute the radius value in the above equation, we will get<br \/>\nA = 3\u221a3\/ 2 (21)\u00b2.<br \/>\nA = 3\u221a3\/ 2 (441).<br \/>\nA = 1145.75<br \/>\nThe area of the hexagon is equal to 1145 cm\u00b2.<br \/>\nArea of the shaded region = Area of the large geometrical shape \u2013 Area of the small geometrical shape.<br \/>\nArea of the shaded region = 1386 \u2013 1145 = 241 cm\u00b2.<br \/>\nTherefore, the area of the shaded region is equal to 241 cm\u00b2.<\/p>\n<p><strong>Problem 2.<\/strong><\/p>\n<p>The square is inscribed in a rectangle. The side of the square is 2cm. The length and breadth of the rectangle is 4cm and 5cm. Find out the area of the shaded region?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-79922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Shadded-Region-for-a-Square-Inscribed-in-a-Rectangle.png\" alt=\"Shadded Region for a Square Inscribed in a Rectangle\" width=\"337\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Shadded-Region-for-a-Square-Inscribed-in-a-Rectangle.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Shadded-Region-for-a-Square-Inscribed-in-a-Rectangle-300x197.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>As per the given details,<br \/>\nThe Square is inscribed in a rectangle.<br \/>\nSide of the square a = 2cm.<br \/>\nLength of the rectangle (l) = 4cm and breadth of the rectangle (b) =5cm.<br \/>\nArea of the square (A) = a\u00b2<br \/>\nSubstitute the \u2018a\u2019 value in the above equation, we will get<br \/>\nArea of the square (A) = (2)\u00b2 = 4cm\u00b2.<br \/>\nArea of the rectangle (A) = l * b<br \/>\nSubstitute the length and breadth values in the above equation, we will get<br \/>\nArea of the rectangle (A) = 4cm * 5cm = 20 cm\u00b2.<br \/>\nArea of the shaded region = Area of the large geometrical shape \u2013 area of the small geometrical shape.<br \/>\nArea of the shaded region = 20 \u2013 4 = 16 cm\u00b2.<\/p>\n<p>Therefore, the Area of the shaded region is equal to 16cm\u00b2.<\/p>\n<p><strong>Problem 3.<\/strong><\/p>\n<p>A Triangle is inscribed in a Square. The side of the square is 20cm and the radius of the triangle is 7cm. Calculate the area of the shaded region?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-79913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Shaded-Region-for-a-Triangle-Inscribed-in-a-Square.png\" alt=\"Shaded Region for a Triangle Inscribed in a Square\" width=\"247\" height=\"257\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>As per the given information,<br \/>\nA triangle is inscribed in a square.<br \/>\nSide of the square (a) = 20cm.<br \/>\nRadius of the triangle (r) = 7cm.<br \/>\nArea of the square (A) = a\u00b2.<br \/>\nSubstitute the \u2018a\u2019 value in the above equation, we will get<br \/>\nArea of the square (A) = (20)\u00b2 = 400cm\u00b2.<br \/>\nArea of the triangle (A)=\u03c0r\u00b2.<br \/>\nSubstitute the radius value in the above equation. Then we will get,<br \/>\nA = 22 \/ 7 (7)\u00b2.<br \/>\nA = 22 * 7 =154.<br \/>\nThe area of the triangle is equal to 154 cm\u00b2.<br \/>\nArea of the shaded region = Area of the large geometrical shape \u2013 area of the small geometrical shape.<br \/>\nArea of the shaded region = 400 \u2013 154 = 246 cm\u00b2.<\/p>\n<p>Therefore, the Area of the shaded region is equal to 246 cm\u00b2.<\/p>\n<p><strong>Problem 4.<\/strong><\/p>\n<p>A semi-circle is inscribed in a square with a radius of 14cm. The side of the square is 25cm. Calculate the area of the shaded region?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-79912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Semi-Circle-inscribed-in-a-Square-Shaded-Region.png\" alt=\"Semi Circle inscribed in a Square Shaded Region\" width=\"267\" height=\"196\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>As per the given details,<br \/>\nA semi-circle is inscribed in a square.<br \/>\nRadius of the semi-circle (r) = 14cm.<br \/>\nSide of the square (a) = 25cm.<br \/>\nArea of the square (A) = a\u00b2.<br \/>\nSubstitute the \u2018a\u2019 value in the above equation, we will get<br \/>\nArea of the square (A) = (25)\u00b2 = 625 cm\u00b2.<br \/>\nArea of the Semi \u2013 circle (A) = \u03c0r\u00b2 \/ 2.<br \/>\nSubstitute the radius of the semi-circle in the above equation, we will get<br \/>\nA = 22 \/ 7 (14)\u00b2 \/ 2.<br \/>\nA = 22 \/ 7 (14 * 14) \/ 2.<br \/>\nA = 22 (2 * 14) \/ 2.<br \/>\nA = 22 * 14 = 308.<br \/>\nThe area of the semi-circle is equal to 308 cm\u00b2.<br \/>\nArea of the shaded region = Area of the large geometrical shape \u2013 Area of the small geometrical shape.<br \/>\nArea of the shaded region = 625 \u2013 308 = 317 cm\u00b2.<\/p>\n<p>So, the Area of the shaded region is equal to 317 cm\u00b2.<\/p>\n<h3>FAQs on finding the Area of a Shaded Region<\/h3>\n<p><strong>1. What is the Area of the Shaded Region?<\/strong><\/p>\n<p>It is the difference between the area of the outer region and the inner region.<\/p>\n<p><strong>2. How to find the Area of the Shaded Region?<\/strong><\/p>\n<p>There are three steps to find the area of the shaded region. They are<br \/>\ni. Calculate the area of the outer region.<br \/>\nii. Calculate the area of the inner region.<br \/>\niii. Subtract the area of the inner region from the outer region.<\/p>\n<p><strong>3. What is the Formula for the Area of the Shaded Region?<\/strong><\/p>\n<p>The formula for the area of the shaded region is<br \/>\nArea of the shaded region = Area of the large geometrical shape (entire region) \u2013 area of the small geometrical shape (shaded region).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The area of the shaded region is the difference between two geometrical shapes which are combined together. By subtracting the area of the smaller geometrical shape from the area of the larger geometrical shape, we will get the area of the shaded region. Or subtract the area of the unshaded region from the area of &#8230; <a title=\"Find the Area of the Shaded Region &#8211;  Simple and Easy Method\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/find-the-area-of-the-shaded-region\/\" aria-label=\"More on Find the Area of the Shaded Region &#8211;  Simple and Easy Method\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":79400,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Find-the-Area-of-Shaded-Region.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/79396"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=79396"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/79396\/revisions"}],"predecessor-version":[{"id":91969,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/79396\/revisions\/91969"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/79400"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=79396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=79396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=79396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}