Question

Think About a Plan

The gazebo in the photo is built in the shape of a regular octagon. Each side is 8 ft long, and the enclosed
area is 310.4 ft2. What is the length of the apothem?
• How can you draw a diagram to help you solve the problem?
• How can you use the area of a regular polygon formula?

Answer 1

9.7 ft

Explanation:

Use the formula for the area of a regular polygon with "n" sides with lengths "s" and apothem a:

A= 1/2 ans

1. Substitute A= 310.4

2. n= 8 (for octagon)

3. s = 8 (length of side)

310.4 = 1/2 (a)(8)(8)

310.4= 32a

a= 9.7 ft

Length of apothem: 9.7 ft