Question

The base of a regular pyramid is a hexagon.

The figure shows a regular hexagon with center C. An apothem is shown as a dashed segment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 8 centimeters. The angle formed by the edge and the segment measures 60 degrees.



What is the area of the base of the pyramid?

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

Answer 1

The answer is 96√3 cm²

Answer 2

`216√(3)`
`cm^(2)`

Explanation:

Length of edge:

`12`

Length of apothem:

`(√(3))/(2)*12`

`6√(3)`

3 × Length of edge × Length of apothem:

`3*12*6√(3)`

`216√(3)`