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 = ¼*

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


Area of Pentagon is given by 5/2 * s * 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.

Example 1 :

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

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

= 5/2 * 5* 2

=25 square centimeteres.

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

Solution :


s = 5 cm

a = 3 cm

Area of a pentagon

= 37.5 cm

II. Divide the regular pentagon into five equal triangles.


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

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

Perimeter of Pentagon


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Identify the following figure: