The base of a regular hexagonal pyramid has an apothem length of 3√ in. What is the exact area of the base of the pyramid?

B = ? cm²

1. To solve this problem you must apply the formula for calculate the area of a regular hexagon given the apothem, which is shown below:

A = (Perimeter x Apothem) / 2

2. You have the apothem, so you can calculate the perimeter. First, you have to know the lenghts of the sides:

Tan (30°) = x/√3

x=1

Side=2x

Side=2

Perimeter=2x6

Perimeter=12

3. Then, you have that the area of the base is:

A = (Perimeter x Apothem) / 2

A=12x√3/2

A=6√3

A=10.39

B=10.39 cm²

The answer is: B=10.39 cm²