Question

The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid? Express your answer in radical form.

Answer 1

Area of hexagon is `216sqrt(3)` `cm^2`

Explanation:

We know that the angle at `C` is 30 degrees, so half of the base must be `12/2` which is `6` as `sin(pi/6)=1/2`.
Finding `a` is a matter of Pythagorean,

as such `a^2+6^2=12^2`

or `a^2=144-36=108` and

`a=sqrt108=sqrt(6xx6xx3)=6sqrt(3)`.

Now, we have the height and half of the base, which means the area of `1/6`th of the hexagon will be `1/2bh` where `b=12` and `h=6sqrt3`.

The area of the hexagon therefore will be `6xx1/2bh`.

`=6xx1/2xx12xx6sqrt(3)=216sqrt(3)` `cm^2`