Skill: Calculate the volume of prisms

A prism has the same cross-section all the way through. To find its volume, use

$$V=Bh$$

where:

• $B$ is the area of one base (the uniform cross-section)
• $h$ is the perpendicular length of the prism

The base does not have to be the bottom face. Choose the face whose area is easiest to calculate.

Example: A triangular prism has triangular bases with a base of $6\text{ cm}$ and a perpendicular height of $4\text{ cm}$. The prism is $10\text{ cm}$ long. Find its volume.

Step 1: Find the area of the triangular base.

The area of a triangle is

$$B=\frac{1}{2}bh$$

Substitute the triangle’s dimensions:

$$B=\frac{1}{2}(6)(4)=12\text{ cm}^2$$

Step 2: Multiply the base area by the prism’s perpendicular length.

$$V=Bh$$ $$V=(12)(10)=120\text{ cm}^3$$

Therefore, the volume of the triangular prism is

$$\boxed{120\text{ cm}^3}$$

Remember to use square units for area and cubic units for volume.