# Area of A Pentagon

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A pentagon is a geometric figure which belongs to the polygon group of geometric shapes. If a polygon has ‘5’ sides, then that polygon is called apentagon. A regular pentagon is the pentagon whose length of the sides are equal to each other. Area of a pentagon is the area covered inside the shape by its sides and can be calculated using its side lengths.

Example 1: Calculate the area of a regular pentagon, given the side length equal to 12m and the length of its apothem equal to 9m.

In order to find the area of the regular pentagon, we can use the given side length and the apothem.

Area of a regular pentagon, A = 1/2 * (apothem) * (Perimeter of the pentagon)

Given length of the apothem = 9m
Perimeter of the regular pentagon= Sum of all sides of the pentagon= 5* s= 5* 12 = 60m
Hence area of the regular pentagon, A = 1/2 * 9m * 60m

A = 30 * 9 = 270m2

Example 2:Calculate the area of a regular pentagon, given the side length equal to 15m and the length of its apothem equal to 6m.

In order to find the area of the regular pentagon, we can use the given side length and the apothem.

Area of a regular pentagon, A = 1/2 * (apothem) * (Perimeter of the pentagon)

Given length of the apothem = 6m
Perimeter of the regular pentagon= Sum of all sides of the pentagon= 5* s= 5* 15 = 75m
Hence area of the regular pentagon, A = 1/2 * 6m * 75m

A = 3 * 75 = 225m2