In this video, we are going to look at how to calculate the area of a regular polygon using the apothem.

A line drawn from the center of a shape to one of the sides that also acts as the perpendicular line. It splits the side equally in half, forming right angles.

Let’s label the apothem “a”. The formula to find the area of a regular polygon using the apothem is:
$A=\frac{1}{2}(a)(P)$

For example:
A pentagon has a side length of 3 inches with an apothem measuring at 2.5 inches. Determine the area of the pentagon.

Substitute the values for apothem and perimeter.
$a=2.5$
$P=5(3)=15$
$A=\frac{1}{2}(2.5)(15)$

Multiply across
$A=18.75$
The area of the pentagon is 18.75 square inches.