At the base of the triangular pyramid lies a right-angled triangle with legs 12 cm and 8 cm.

At the base of the triangular pyramid lies a right-angled triangle with legs 12 cm and 8 cm. The height of the pyramid is 10 cm. Find the volume of this pyramid.

To find the volume of a triangular pyramid, use the following formula:
V = 1/3 * S main * H.
The height of the pyramid is known by condition, we find the area of a right-angled triangle, which is the base of this pyramid:
S main = 1/2 * a * b = 1/2 * 12 * 8 = 48 (cm²).
V = 1/3 * 48 * 10 = 160 (cm³).
Answer: the volume of the pyramid is 160 cm³.