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

The area of the enclosed gazebo is
`310.4\ ft^(2)`

Explanation:

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

we know that

The area of a regular polygon is equal to

`A=(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=(1)/(2)(64)(9.7)`

`A=310.4\ ft^(2)`