Volume of Triangular Prism Formulas | List of Volume of Triangular Prism Formulas You Should Know - BYJUS

# Volume of Triangular Prism Formula

The volume of a triangular prism can be defined as the space occupied by it. A triangular prism is made of two congruent bases, three flat rectangular side faces, and the same cross-section all along its length....Read MoreRead Less

### Formula for the Volume of a Triangular Prism

The formula for the volume of a triangular prism is given by,

V = B x h, where B is the base area and h is the height. The term ‘B’ is the base area and this can be calculated as,

$$B=\frac{1}{2}~\times~base~\times~height~of~the~triangle$$.

Hence, the volume of a triangular prism can also be written as,

$$V=\frac{1}{2}~\times~base(a)~\times~height(c)~\times~prism~height(h)$$ cubic units.

⇒ $$V=\frac{1}{2}~\times~a~\times~c~\times~h$$  cubic units. ### Solved Examples

Example 1: Find the volume of a triangular prism with a base area of 12 $$cm^2$$ and with a height of 6 cm.

Solution

As provided in the question,

The base area, B = 12 $$cm^2$$

Height, h = 6 cm

According to the volume of triangular prism formula,

V = B x h

By substituting the values,

V = 12 x 6

V = 72 $$cm^3$$

So, the volume of the triangular prism is 72 cubic centimeters.

Example 2: Determine the volume of a triangular prism in which the base of the triangle is 8 inches, the height is 6 inches and the length of the prism is 12 inches.

Solution: Details that are stated,

The base of the triangle, a = 8 inches

Height of the triangular base, c = 6 inches

So, the base area $$B=\frac{1}{2}~\times~base~(a)~\times~height~(c)$$

$$B=\frac{1}{2}~\times~8~\times~6$$

$$B=\frac{48}{2}$$

B = 24 $$in^2$$

Length of the prism or height of the prism, h= 12 inches

According to the formula for the volume of a triangular prism,

V = B x h

V = 24 x 12

V = 288 $$in^3$$

Hence, the volume of the triangular prism is 288 cubic inches.

Example 3: Amanda bought a triangular prism as a paper weight. The altitude of the base is 5 cm, edge length is 8 cm, and height of the prism is 6 cm. Find the volume of this triangular prism.

Solution

Provided in the question is,

a = 8 cm c = 5 cm, h = 6 cm

According to the formula,

Volume of triangular prism V = $$\frac{1}{2}~\times~a~\times~c~\times~h$$

V = $$\frac{1}{2}~\times~8~\times~5~\times~6$$

V = $$\frac{1}{2}~\times~240$$

V = 120 $$cm^3$$

So, the volume of the triangular prism that Amanda bought is 120 cubic centimeters.