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

See below.

Explanation:

The triangle shown is a 30-60-90 triangle.

The hypotenuse has length `12` cm

So `a = sqrt3/2 * 12 - 6sqrt3` cm

The other side (the base) of the triangle has length `1/2*12 = 6` cm

If we put a copy of the shown triangle next to it, sharing side `a`, then we get an equilateral tirangle with base 12 and height `6sqrt3`

The are of that equilateral triangle is `1/2(12)(6sqrt3) = 36sqrt3` cm`""^2`

The hexagon has 6 sides, so there are 6 of those equilateral triangles.

The are of the hexagon is `6 * 36sqrt3 = 216sqrt3` cm`""^2`