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 al 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
al 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 al 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. al 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 )
: (2)2 * 8 / 4 tan ( 180 / 8 )
3.31 inches2


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