Question

PLEASE HELP ASAP!!

The base of a regular pyramid is a hexagon.




What is the area of the base of the pyramid?

Enter your answer in the box. Express your answer in radical form.

cm²

Answer 1

The area of the hexagon is
`96√(3)\ cm^(2)`

Explanation:

we know that

The area of the hexagon is equal to

`A=(1)/(2)Pa`

where

P is the perimeter of the hexagon

a is the apothem

Find the Perimeter P

`P=6(8)=48\ cm`

Find the apothem a

`a=(8)sin(60\°)`

`a=8((√(3))/(2))=4√(3)\ cm`

Find the area of the hexagon

`A=(1)/(2)(48)(4√(3))=96√(3)\ cm^(2)`