Question

Which of the following expressions represents the area, in square meters, of the regular decagon (10-sided polygon) with 3.25 meter-sides and a 5-meter apothem.

Answer 1

A = P * a / 2

A = 81.25

Explanation:

We have that there is a corresponding formula for a regular decagon, which depends on the apothem and the perimeter, it is the following:

A = P * a / 2

In this case, the perimeter is the sum of all the sides, that is, 10 sides, therefore:

P = 10 * 3.25

P = 32.5 meters

We replace:

A = 32.5 * 5/2

A = 81.25

Which means that for that regular decagon, the area is 81.25 square meters.