A pentagon is five-sided polygon in geometry. It may be simple or self â€“ 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 =Â $\frac{5}{2}$sa

Where,

s is the side of the pentagon.

a is the apothem length.

### Solved Examples

**QuestionÂ 1:**Find the area of a pentagon of side 10 cm and apothem length 5 cmÂ ?

**Solution:**

Given,

s = 10 cm

a = 5 cm

= $\frac{5}{2}$Â sa

= $\frac{5}{2}$ $\times$ 10 $\times$ 5 cm

^{2 }= 125 cm

^{2}