slaggingV

2020-12-16

The gazebo in the photo is built in the shape of a regular octagon. Each side is 13ft long and the enclosed area is $816.4f{t}^{2}$
What is the length of the apothem?

Gennenzip

Use the formula for the area of a regular polygon with nn sides with length ss and apothem a:
$A=\frac{1}{2}ans$
Substitute $A=816.4f{t}^{2}$, n=8, and s=13 ft: $816.4=\frac{1}{2}\left(a\right)\left(8\right)\left(13\right)$
816.4=52a
15.7=a
So, the length of the apothem is 15.7 ft.

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