# Area of Pentagon

A Pentagon is a five-sided polygon in geometry. It can be regular as well as irregular. The sides and angles of a regular pentagon are equal with each interior angle equals to 108 degrees, and its exterior angle is equal to 72 degrees. The number of diagonals in a Pentagon are five.

Formula for no. of diagonals is given {n*(n-3)}/2 where n=5

## Area of Pentagon

Area of a pentagon, $A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}$

This formula is for any pentagon, whether it is regular or irregular.

Area of regular pentagon can be found out in 2 ways.

Area of Pentagon is given by 5/2 x s x a; where s is the side of the Pentagon, and a is the apothem length.

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

### Examples

Example 1 : Let’s take the pentagon with side length 5 units and apothem length 2 units

Area of pentagon is = 5/2 x s x a

= 5/2 x 5 x 2

=25 square centimetres.

Example 2 : Find the area of a pentagon of side 5 cm and apothem length 3 cm ?

Solution :

Given,

s = 5 cm

a = 3 cm

Area of a pentagon

= 37.5 cm

### How to Find Area of Pentagon?

II. Divide the regular pentagon into five equal triangles.

Area of triangle is given by = ½ x base x height

Area of Pentagon is given by = 5 x Area of triangle

### Perimeter of Pentagon

This is all about PENTAGON.To know more about the various attributes of Pentagon and other