Area of a Regular Polygon Area of a Regular Polygon In mathematics, the word polygon comes from Greek word polus-gonia. This is formed by two words ‘polus’ and ‘gonia’. In the Greek the word polus refers to the much or many and in the same aspect the word gonia refers to the angle. The polygon can be considered as a basic shape of the geometry which is formed on 2 - D plane. Polygons are the shape which is formed by the straight lines but the sides of the polygon must be interlinked to each other. In geometrical mathematics, a polygon can be defined as a geometrical figure that is considered in the closed shape with straight lines. In a simple mean we can say that the polygon as a closed figure that are made up of several lines segment that are interlinked to each other. In the shape of polygon different straight lines are interconnected to each other, these sides are popularly known as edges of the polygon. According to properties of the polygon we can categorize the polygon into three different categories. The most popular types of polygons are Convex and Concave, Simplex or complex and Regular and irregular.
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A regular polygon is a polygon that has the concept of equilateral or equiangular. The word Equiangular with regular polygon refers that all the angles of polygon are equal in measure. In the same aspect we can say that the word equilateral refers to the shape when polygon has all sides of the same length. According to the above given properties we can easily define the regular polygon as the shape where all the angles are equal in measure and all the sides are the same length. It means to say that regular polygon follow the concept of equiangular and equilateral. As like the other geometrical shape, the regular polygon has their surface area into it. In mathematics to calculate the area of regular polygon the formula are define for the area of regular polygon. The area of regular polygon can easily be calculated when we have the value of the given regular polygon sides. As we know that in the regular polygon all the sides of the polygon are equal in length. In the case when we get the value of one of the side then we can easily calculate the area of the regular polygon by the below given formula: Formula for Area of a Regular Polygon: (Side)2 * n / 4 tan ( 180 / n ) In the above formula we use the several symbols which is used for denoting several things that helps in calculating the area of regular polygon. In the above formula the side refers to the value of the side. In the same aspect the symbol ‘n’ is used for denoting the number of sides in the polygon. Tan is the tangent function which is used to calculate the value in the form of degree. Now we show you some of the examples that help in understanding the concept of area of regular polygon.
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Example: suppose there is an polygon which has eight sides into it. all the sides are equal to each other. The length of one side is equal to the 2 inches. Calculate the area of regular polygon? Solution: Given that Length of the side is = 2 inches By applying the formula for calculating the area of regular polygon: (Side)2 * n / 4 tan ( 180 / n ) รฐ
: (2)2 * 8 / 4 tan ( 180 / 8 )
รฐ
3.31 inches2
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