Volume of a Triangular Prism

Volume of a Triangular Prism

A triangular prism has two matching triangular bases and a length between them. To find its volume, first find the area of the triangular base, then multiply by the prism’s length.

1. Find the area of the triangle

Use the triangle’s base and height:

[ A = \frac{1}{2}bh ]

Here, (b) is the base of the triangle and (h) is the perpendicular height of the triangle, not the slanted side.

2. Multiply by the prism length

Once you know the triangle’s area, multiply by the prism’s length (L):

[ V = A \cdot L ]

So the full volume formula is:

[ V = \left(\frac{1}{2}bh\right)L ]

3. Simplify carefully

If the numbers allow, simplify before or after multiplying. Keep units cubed, such as (\text{cm}^3) or (\text{m}^3).

4. Check your work

• Make sure the triangle height is perpendicular to its base.
• Confirm you used the prism length, not another side.
• Volume should be in cubic units.

A good final check is to estimate the answer: the volume should be the area of one triangular face times the prism’s length.