Calculate the volume of a regular triangular prism, the base side of which is 14 cm, and the height is 6 cm.

Prism volume:

V = S * h, where S is the area of the base of the prism (regular equilateral triangle), h is the height of the prism (h = 6 cm).

The area of a triangle can be calculated using Heron’s formula:

S = √ (p (p – a) (p – b) (p – c)), where p is the semiperimeter of the triangle; a, b, c – the lengths of the sides of the triangle.

Since the sides of the triangle are equal, the formula will take the form:

S = a ^ 2 * √3 / 4, where a = 14 cm.

Prism volume:

V = S * h = (a ^ 2 * √3 / 4) * h = (14 ^ 2 * √3 / 4) * 6 = 509.22 cm3.

Answer: The volume of the prism is 509.22 cm3.