Find the volume of a regular triangular pyramid of the base side of which is 12 cm, and the height of the pyramid is 6 cm.

Since the pyramid is regular, at its base there is an equilateral triangle with a side of 12 cm.

Determine the area of the base of the pyramid.

Sosn = a ^ 2 * √3 / 4, where a is the side of the triangle.

Sbn = 12 ^ 2 * √3 / 4 = 36 * √3 cm2.

Let’s define the volume of the pyramid.

V = Sbn * h / 3 = 36 * √3 * 6/3 = 72 * √3 cm3.

Answer: The volume of the pyramid is 72 * √3 cm3.