The polygon area is the region occupied by the polygon. The basic types of polygons are regular polygon and irregular polygon. Learn about the area of a polygon, polygon definition, central point of a polygon, radius of the inscribed circle, circumscribed circle, and polygon of n sides.<\/p>\n
Polygon is a closed shape in a two dimensional plane with straight lines. It has an infinite number of sides but all sides are straight lines. The line segments of a polygon are called the sides or edges. The point of intersection of two line segments is called the vertex.<\/p>\n
Based on the sides and angles, the polygons are classified into different types. They are regular polygon, irregular polygon, convex polygon, and concave polygon. The regular polygon measures all sides and angles equal. Some of the polygons are triangle, square, pentagon, hexagon, and others.<\/p>\n
Central Point of a Polygon:<\/strong><\/p>\n The inscribed and the circumscribed circles of a polygon have the same center, called the central point of the polygon.<\/p>\n The radius of the Inscribed Circle of a Polygon:<\/strong><\/p>\n The length of the perpendicular from the central point of a polygon upon any one of its sides is called the radius of the inscribed circle of the polygon. The radius of the inscribed circle of a polygon is denoted by r.<\/p>\n The radius of the Circumscribed Circle of a Polygon:<\/strong><\/p>\n The line segment joining the central point of a polygon to any vertex is the radius of the circumscribed circle of the polygon. The radius of the circumscribed circle of a polygon is denoted by R.<\/p>\n Properties of Polygon<\/strong><\/p>\n The polygon\u2019s properties are based on the sides and angles. Refer to the below properties and learn entirely about Polygons. They are as follows<\/p>\n Follow the below mentioned simple steps and instructions to calculate the area of a polygon having N-Sides easily.<\/p>\n Example 1.<\/strong><\/p>\n Find the area of a regular pentagon whose perimeter is 40 units and whose apothem is 5 units?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n The perimeter of the regular pentagon = 40 units<\/p>\n Apothem = 5 units<\/p>\n Area of the regular pentagon = \u00bd (perimeter) (apothem)<\/p>\n = \u00bd (40) (5)<\/p>\n = 20 x 5 = 100 sq units<\/p>\n Therefore, the area of regular pentagon = 100 sq units.<\/p>\n Example 2.<\/strong><\/p>\n Find the area of a regular octagon each of whose sides measures 25 cm?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n Side of a regular octagon a = 25 cm<\/p>\n Area of octagon A = 2a\u00b2 (1 + \u221a2)<\/p>\n Substitute a = 25 in above equation.<\/p>\n A = 2 x 25\u00b2 (1 + \u221a2)<\/p>\n = 2 x 625 (1 + \u221a2) = 1250 (1 + \u221a2)<\/p>\n = 1250 x 2.414 = 3,017.76 cm\u00b2<\/p>\n Therefore, regular octagon area is 3017.76 cm\u00b2.<\/p>\n Example 3.<\/strong><\/p>\n The area of a regular pentagon is 215 cm\u00b2. Find the length of the side of the pentagon?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n Regular pentagon area A = 215 cm\u00b2<\/p>\n Pentagon area formula is 1\/4 ((\u221a(5 (5 + 2 \u221a5) s\u00b2))<\/p>\n Pentagon area = 215 cm\u00b2<\/p>\n 1\/4 ((\u221a(5 (5 + 2 \u221a5) s\u00b2)) = 215<\/p>\n (\u221a(5 (5 + 2 \u221a5) s\u00b2)) = 215 x 4 = 860<\/p>\n s\u00b2 = 860\/(\u221a(5 (5 + 2 \u221a5))<\/p>\n s\u00b2 = 860\/6.88 = 125<\/p>\n s = \u221a125<\/p>\n s = 11.18<\/p>\n Therefore, side of regular pentagon is 11.18 cm.<\/p>\n Example 4.<\/strong><\/p>\n Find the area of a regular polygon having 12 sides and each side length is 5 m?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n Number of sides of a polygon n = 12<\/p>\n Side length a= 5 cm<\/p>\n Area of regular polygon A = [n * a\u00b2 * cot(\u03c0\/n)]\/4<\/p>\n A = [12 x 5\u00b2 x cot(\u03c0\/12)]\/4<\/p>\n = [12 x 25 x (2 + \u221a3)]\/4<\/p>\n = (300 x (2 + \u221a3))\/4<\/p>\n = 75 (2 + \u221a3)<\/p>\n = 75 (3.73) = 279.9 cm\u00b2<\/p>\n Therefore, the area of a regular polygon is 279.9 cm\u00b2.<\/p>\n","protected":false},"excerpt":{"rendered":" The polygon area is the region occupied by the polygon. The basic types of polygons are regular polygon and irregular polygon. Learn about the area of a polygon, polygon definition, central point of a polygon, radius of the inscribed circle, circumscribed circle, and polygon of n sides. Types of Polygons Polygon is a closed shape … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35609"}],"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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35609"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35609\/revisions"}],"predecessor-version":[{"id":92624,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35609\/revisions\/92624"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35609"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35609"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Area of Regular Polygons Formulas<\/h3>\n
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How to Find the Area of N- Sided Polygons?<\/h3>\n
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Area of a Polygon Word Problems<\/h3>\n