# Area of a Pentagon Formula

A pentagon is five-sided polygon in geometry. It may be simple or self – intersecting in shape. The five angles present in the pentagon are equal. A regular pentagon has all of the sides and angles are the same as each other. Pentagons can be regular or irregular and convex or concave. A regular pentagon is one with all equal sides and angles. Its interior angles are 108 degrees and its exterior angles are 72 degrees. An irregular pentagon is a shape that does not have equal sides and/or angles and therefore do not have specified angles. A convex pentagon is one whose vertices, or points where the sides meet, is pointing outwards as opposed to a concave pentagon whose vertices point inwards. Imagine a collapsed roof of a house.

The Area of a Pentagon Formula is, A = $\frac{5}{2}$sa
Where,
s is the side of the pentagon.
a is the apothem length.

### Solved Examples

Question 1: Find the area of a pentagon of side 10 cm and apothem length 5 cm ?
Solution:
Given,
s = 10 cm
a = 5 cm
Area of a pentagon
= $\frac{5}{2}$ sa
= $\frac{5}{2}$ $\times$ 10 $\times$ 5 cm2
= 125 cm2
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