The side edge of a regular hexagonal pyramid is 20, the side of the base is 10. Find the volume of the pyramid.

It is known:

Hexagonal pyramid;

Side rib = 20;

Base side = 10.

Let’s calculate the volume of the hexagonal pyramid.

1) First, we find the area of the base. The base is a hexagon.

Find by the formula S = 3√3 / 2 * a ^ 2;

Substitute the known values and then we get the base area.

S = 3√3 / 2 * 10 ^ 2 = 3√3 / 2 * 100 = 3√3 * 50 = 150√3.

2) The volume of the hexagonal pyramid is found by the formula:

V = 1/3 * Sosn * h;

3) Substitute the known values into the formula V = 1/3 * Sb * h and calculate the volume.

V = 1/3 * 150√3 * 20 = 50√3 * 20 = 1000√3.