# Volume of a Triangular Pyramid

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A pyramid is a 3-dimensional geometric structure which consists of a base and the height. There are different types of pyramids depending on the type of base the pyramid has, like a square base or a rectangular base. A pyramid with a triangular base is known as the triangular pyramid and we can find its surface area and its volume. Volume of a triangular pyramid is equal to the product of one-third the area of the base and its height.

Example 1: Calculate the volume of a triangular pyramid whose triangular base length is 5m, height of the base triangle is 4m and the height of the pyramid is 9m.

Given base length of the pyramid, b= 5m

Height of the base triangle, h= 4m

Height of the pyramid, H= 9m

Volume of the pyramid, V= 1/3* Area of the base* Height of pyramid

Area of the triangular base= 1/2* b* h = 1/2* 5m* 4m= 10m2

Volume of the triangular pyramid, V= 1/3* 10m 2 * 9m= 30m3

Therefore, volume of the given triangular pyramid, V= 30m3

Example 2: Calculate the volume of a triangular pyramid whose triangular base length is 4m, height of the base triangle is 3m and the height of the pyramid is 8m.

Given base length of the pyramid, b= 4m

Height of the base triangle, h= 3m

Height of the pyramid, H= 8m

Volume of the pyramid, V= 1/3* Area of the base* Height of pyramid

Area of the triangular base= 1/2* b* h= 1/2* 4m* 3m= 6m2

Volume of the triangular pyramid, V= 1/3 *6m 2 * 8m= 16m3

Therefore, volume of the given triangular pyramid, V= 16m3