The gazebo in the photo is built in the shape of a regular octagon. Each side is 6 ft long, and the enclosed area is 172.8 ft². What is the length of the apothem?

Kaycee Roche

Kaycee Roche

Answered question

2021-01-06

The gazebo in the photo is built in the shape of a regular octagon. Each side is 6 ft long, and the enclosed area is 172.8 ft². What is the length of the apothem?

Answer & Explanation

Usamah Prosser

Usamah Prosser

Skilled2021-01-07Added 86 answers

Use the formula for the area of a regular polygon with nn sides with length ss and apothem aa:
A=12ans
Substitute A=172.8ft2, n=8 (for octagon), and s=6 ft:
172.8=12(a)(8)(6)
172.8=24a
7.2=a
So, the length of the apothem is 7.2 ft.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

Answer is given below (on video)

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