Question

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

`96 √(3) {cm}^(2)`

Step-by-step explanation

The area of a regular polygon is

`Area= (1)/(2) ap`

where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.

From the diagram,

`\sin(60) = (a)/(8)`

a=8sin(60)

`a = 4 √(3)`

`\cos(60) = (l)/(8)`

`l = 8 \cos(60)`

`l = 4`

The length of one side of the hexagon is 2×4=8.

The perimeter of the hexagon is

p=6×8=48

The area of the hexagon is

`= (1)/(2) * 4 √(3) * 48`

`= 96 √(3) {cm}^(2)`