Area of Pentagon

Area of Pentagon:

The pentagon is a five-sided polygon and a two dimensional geometrical figure.  Its name is derived from the Greek words ‘penta’ which means ‘five’ and ‘gon’ which means ‘angles’

What is the area of the pentagon?

The area of a pentagon is the space that is covered within the sides of the pentagon.

It can be calculated by various methods depending on the dimensions that are known.

It also depends on the type of pentagon.

For example, 

Regular pentagon, then the area can be calculated with the help of one single formula, but if it is an irregular pentagon, then we need to split it into different polygons and add their areas to get the area of the pentagon.

The area of a pentagon is expressed in square units.

Area of pentagon formula:

The formula that is used to find the area of a pentagon varies according to the type of pentagon.

The area of a pentagon formula that is commonly used to find the area of a regular pentagon is,

Area of pentagon= (1 / 2)p.a     

‘p’ is the perimeter and ‘a’ is the apothem of the pentagon.

Examples of the area of the pentagon

Example:

Find the area of regular pentagon if the length of the side of the pentagon is 10 inches and the length of the apothem is 6.88 inches

Solution:

     Given, s=10, and a=6.88 

The formula to find the area of a pentagon with apothem is,

Area of pentagon= (1 / 2).p.a

= 1 / 2 10 56.88 = 147.