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

Since, by condition, the pyramid is regular, an equilateral triangle lies at its base. Determine the area of the base of the pyramid.

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

Sb = 6 ^ 2 * √3 / 4 = 36 * √3 / 4 = 9 * √3 cm2.

Let’s define the volume of the pyramid.

V = Sn * h / 3 = 9 * √3 * 12/3 = 36 * √3 cm3.

Answer: The volume of the pyramid is 36 * √3 cm3.