{"id":4715,"date":"2023-04-28T10:00:03","date_gmt":"2023-04-28T04:30:03","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=4715"},"modified":"2023-04-29T10:00:45","modified_gmt":"2023-04-29T04:30:45","slug":"find-area-plane-figure","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/find-area-plane-figure\/","title":{"rendered":"How To Find The Area Of A Plane Figure"},"content":{"rendered":"<h2><strong>How To Find The Area Of A Plane Figure<\/strong><\/h2>\n<p>The area of the portion of the plane or shape can be defined as the amount of stuff required to cover it.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12099\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/10\/find-area-plane-figure-1.png\" alt=\"\" width=\"746\" height=\"429\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/10\/find-area-plane-figure-1.png 746w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/10\/find-area-plane-figure-1-300x173.png 300w\" sizes=\"(max-width: 746px) 100vw, 746px\" \/><\/p>\n<p>For finding the area of a polygon, we consider the enclosed region of the polygon.\u00a0Let us consider an illustration to clarify the idea.<\/p>\n<p>A news bulletin board in a class is to be covered with squared colour paper sheets. To know that how many colour paper sheets are required for the said purpose, the best way is to lay the board on the floor and cover it with a coloured paper sheet without any gap as shown in the figure.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c2.staticflickr.com\/6\/5245\/29994983872_db2fa630dd_o.png\" alt=\"Area-Of-Plane-Figure\" width=\"398\" height=\"151\" \/><\/p>\n<p>Count the number of sheets used for this purpose. Suppose 21 sheets are used to cover the complete board, then, we can measure the region enclosed by a polygon. This measurement is called the area of the polygon.<br \/>\n\u2234 Area = 21 \u00d7\u00a0Area of 1 sheet<br \/>\nThe amount of surface enclosed by a plane figure is called its area. It is measured in square units of lengths.<\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/9Zt0IK7Jmk8?start=55&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h3><strong>To find the area of a figure using a graph<\/strong><\/h3>\n<p>We can find the area of regular and irregular figures by using a graph or squared paper. To find the area, first we draw the figure on the graph paper covering as many squares as possible.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c2.staticflickr.com\/6\/5795\/29814306580_26016176e7_o.png\" alt=\"area-of-figure-using-graph\" width=\"490\" height=\"334\" \/>For finding the area by using squared paper, we have to follow the following steps:<\/p>\n<ol>\n<li>Count the number of complete squares of unit length enclosed by the figure.<\/li>\n<li>Count the number of those squares whose more than half parts are enclosed by the figure.<\/li>\n<li>Count the number of those squares whose exact half parts are enclosed by the figure and divide the number by 2.<\/li>\n<li>Leave those squares whose less than half parts are enclosed by the figure.<\/li>\n<li>The total of steps (i), (ii), and (iii) are added to obtain the area of the figure.<\/li>\n<\/ol>\n<p>\u2234 Area of the figure = Number of complete squares + Number of squares having more than half parts enclosed + 1\/2 (Number of squares having half parts enclosed)<\/p>\n<p>Consider the figures given in figure.<br \/>\n<strong>(i)<\/strong> Area of rectangle ABCD<br \/>\n= 8 \u00d7 Area of one square<br \/>\n= 8 \u00d7 1 cm<sup>2<\/sup> = 8 cm<sup>2<\/sup><br \/>\nThus, if the length and breadth of a rectangle are 4 cm and 2 cm respectively, then<br \/>\nArea = 8 cm<sup>2<\/sup><br \/>\n= (4 \u00d7 2) sq cm<br \/>\n\u2234 Area = length \u00d7 breadth<\/p>\n<p><strong>(ii)<\/strong> Area of \u0394PQR = Number of complete square + Number of squares having more than half parts + 1\/2 \u00d7 Number of halved squares<br \/>\nNumber of complete squares enclosed in the figure = 2<br \/>\nNumber of squares whose more than half parts are enclosed = 4<br \/>\nNeglect the number of squares whose less than half part is enclosed.<br \/>\nArea of \u0394PQR = 2 + 4 + 1\/2 \u00d7 0<br \/>\n= 6 squares<br \/>\n= 6 \u00d7 1 cm<sup>2<\/sup><br \/>\n= 6 cm<sup>2<\/sup><br \/>\nThus, if the base and height of the triangle are 4 cm and 3 cm respectively, then<br \/>\nArea = 6 cm<sup>2<\/sup><br \/>\n= 1\/2 \u00d7 4 \u00d7 3<br \/>\n= 1\/2 \u00d7 base \u00d7 height<\/p>\n<p><strong>(iii)<\/strong> Area of square WXYZ<br \/>\n= 9 \u00d7 Area of one square<br \/>\n= 9 \u00d7 1 cm<sup>2<\/sup><br \/>\n= 9 cm<sup>2<\/sup><br \/>\nThus, if the side of the square is 3 cm, then<br \/>\nArea = 9 cm<sup>2<\/sup><br \/>\n= (3 \u00d7 3) cm<sup>2<\/sup><br \/>\n= side \u00d7 side<\/p>\n<p><strong>(iv)<\/strong> Similarly, area of figure ABCDEFGH<br \/>\n= 7 \u00d7 Area of one square<br \/>\n= 7 \u00d7 1 cm<sup>2<\/sup><br \/>\n= 7 cm<sup>2<\/sup><\/p>\n<h2><strong>The Area Of Plane Figures Example Problems with Solutions<\/strong><\/h2>\n<p><strong>Example 1:<\/strong> Find the area of a square whose side is 8 cm.<br \/>\n<strong>Solution:<\/strong> Area of square<br \/>\n= side \u00d7 side<br \/>\n= 8 cm \u00d7 8 cm<br \/>\n= 64 cm<sup>2<\/sup><\/p>\n<p><strong>Example 2:<\/strong> Find the area of a rectangle whose length is 21 cm and breadth is 5 cm.<br \/>\n<strong>Solution:<\/strong> Area of a rectangle<br \/>\n= length \u00d7 breadth<br \/>\n= 21 cm \u00d7 5 cm<br \/>\n= 105 cm<sup>2<\/sup><\/p>\n<p><strong>Example 3:<\/strong> The side of a square plot of land is 30 m. Find the cost of levelling the plot, if the rate is Rs 2 per square metre.<br \/>\n<strong>Solution:<\/strong>\u00a0Area of square<br \/>\n= side \u00d7 side<br \/>\n= 30 m \u00d7 30 m<br \/>\n= 900\u00a0m<sup>2<\/sup><br \/>\nLevelling cost of 1\u00a0m<sup>2<\/sup><br \/>\n= Rs. 2<br \/>\nLevelling cost of 900\u00a0m<sup>2<\/sup><br \/>\n= Rs. (2\u00d7 900)<br \/>\n= Rs. 1800<\/p>\n<p><strong>Example 4:<\/strong> Find the area of the given figure.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8417\/29481705534_29a63fba40_o.png\" alt=\"find-area\" width=\"266\" height=\"315\" \/><br \/>\n<strong>Solution:<\/strong> Area of the rectangle DEFG = l \u00d7 b<br \/>\n= 7 cm \u00d7 3 cm = 21 cm<sup>2<\/sup><br \/>\nArea of the rectangle ABCG \u00a0l \u00d7 b<br \/>\n= 7 cm \u00d7 3 cm = 21 cm<sup>2<\/sup><br \/>\nArea of the complete figure<br \/>\n= Area of rectangle DEFG<br \/>\n= 21 cm<sup>2<\/sup> + 21 cm<sup>2<\/sup><br \/>\n= 42 cm<sup>2<\/sup><\/p>\n<p><strong>Example 5:<\/strong> How many tiles, each measuring 2 m by 1 m, are required to cover a rectangular hall 12 m long and 8 m broad? Find the cost of tiles at Rs. 25 per tile.<br \/>\n<strong>Solution:<\/strong> Length of a tile = 2 m<br \/>\nBreadth of a tile = 1 m<br \/>\n\u2234\u00a0Area of each tile = 2 m \u00d7 1 m<br \/>\n= 2\u00a0m<sup>2<\/sup><br \/>\nLength of rectangular hall = 12 m<br \/>\nBreadth of rectangular hall = 8 m<br \/>\n\u2234\u00a0Area of the hall = 12 m \u00d7 8 m<br \/>\n= 96\u00a0m<sup>2<\/sup><br \/>\nHence, number of tiles required<br \/>\n= Area of the hail\/Area of one tile<br \/>\n= 96\/2 = 48<br \/>\n\u2234 Cost of tiles 48 \u00d7\u00a025<br \/>\n= Rs. 1200<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How To Find The Area Of A Plane Figure The area of the portion of the plane or shape can be defined as the amount of stuff required to cover it. For finding the area of a polygon, we consider the enclosed region of the polygon.\u00a0Let us consider an illustration to clarify the idea. A [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[2724,2726,2725,4567],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How To Find The Area Of A Plane Figure - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/find-area-plane-figure\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How To Find The Area Of A Plane Figure\" \/>\n<meta property=\"og:description\" content=\"How To Find The Area Of A Plane Figure The area of the portion of the plane or shape can be defined as the amount of stuff required to cover it. 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