Calculate the volume of a regular triangular prism if the side of the base is 10 cm and the height of the prism is 12 cm.

Since the pyramid is regular, an equilateral triangle lies at its base, then AB = BC = AC = 10 cm.

Determine the area of the triangle at the base, which is calculated by the formula: S = a ^ 2 * √3 / 4, where a is the length of the triangle.

Savsd = 10 ^ 2 * √3 / 4 = 100 * √3 / 4 = 25 * √3 cm2.

Then the volume of the pyramid is:

Vavsd = Saavsd * OD / 3 = 25 * √3 * 12/3 = 100 * √3 cm3.

Answer: The volume of the pyramid is 100 * √3 cm3.