Find the volume of a regular triangular pyramid if H = 12 and the side is the base 13.

To find the given volume, we calculate one third of the product of the height of the pyramid and the length of the side of the base squared:

V = 1/3 * 12 * 13 ^ 2 = 12/3 * 13 ^ 2.

Reduce the fraction in the expression by 3:

V = 4 * 13 ^ 2 = 4 * 169 = 676 (cm3).

Answer: the volume of a given regular pyramid is 676 (cm3).