volume of a regular hexagon pyramid.

Question

The length of the altitude $h$ of a regular hexagon pyramid is three times the length of the side $s$ of the base. What is the volume of the pyramid in terms of $h$?

Answer 1

Hint:

Remember the formula for a pyramid is $\frac{1}{3} * a * h$. Since we know that $h=3s$, then we have $a * \frac{1}{3} * 3s$, or $as$, where $a$ is the base area, $h$ is the height of the pyramid, and $s$ is the side length of the base.

Now to find the base area, split the hexagon up into $6$ smaller equilateral triangles. You can either use the Pythagorean theorem or trigonometry to calculate the area of one of them. Put this in terms of $h$ and simplify the expression.