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 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 Regular Pentagon

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 pentagon derivation

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

Pentagon

This is all about PENTAGON.To know more about the various attributes of Pentagon and other
geometrical figures, please do visit www.byjus.com or download BYUS-THE LEARNING APP.

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