Question

A family is planning a wedding celebration in a gazebo. They want to know the area so that they can determine how many people can comfortably fit inside. They take some measurements and find that each side is 8 ft long and the apothem is 9.7 ft. What is the area of the enclosed gazebo?​

Answer 1

Answer:

The area of the enclosed gazebo is $310.4\ ft^{2}$

Step-by-step explanation:

I assume that is a regular octagon (eight equal aides)

we know that

The area of a regular polygon is equal to

$A=\frac{1}{2}(P)(a)$

where

P is the perimeter of the polygon

a is the apothem

Find the perimeter P (the octagon has 8 sides)

$P=8(8)=64\ ft$

$a=9.7\ ft$

substitute

$A=\frac{1}{2}(64)(9.7)$

$A=310.4\ ft^{2}$