Question

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?

Answer 1

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