Calculate the area of a regular pentagon with side = 6 inches and apothem = 4 inches.

Question

Calculate the area of a regular pentagon with side = 6 inches and apothem = 4 inches.

Answer 1

The easiest way to calculate the area of difficult shapes is to break them down into easier shapes like triangles.

First, draw your pentagon so its bottom is flat. Draw 2 line segments,

one from the bottom left corner to the center of the pentagon,

one from the bottom right corner to the center of the pentagon.

This makes a triangle. Its height is the apothem, and its base is the pentagon side length, so its area is

1/2 base * height = 1/2 * 6 * 4 = 12 in².

The pentagon can be broken into 5 of these triangles, so the total area must be 5 * 12 = 60 in².

Hope this helps!

~Logan