In this post, we explain how to calculate the area of a pentagon. Here you can find a solved exercise of the area of a pentagon and, in addition, a calculator to calculate the area and the perimeter of any pentagon.
How to calculate the area of a pentagon
The area of a pentagon is equal to the perimeter of the pentagon times its apothem divided by two. Therefore, the area of a regular pentagon is five times the length of its side multiplied by its apothem divided by two.
Therefore, the formula for the area of a regular pentagon is as follows:
Example of the area of a pentagon
Having seen the formula for a pentagon’s area, we will now calculate an example of the area of a pentagon. So you can see how to calculate the area of a pentagon.
Find the area of the regular pentagon whose side is 4 cm and whose apothem is 4 cm.
To find the area of the pentagon, we have to multiply the length of its side by 5 and by the apothem, and then divide by two:
A= (Perimeter x Appthem) / 2
So we substitute the data from the exercise in the formula and calculate the area of the pentagon:
A= (20 x 4) / 2 = 40 cm2
