7th Grade Math

560 Volume and Surface Area

A triangular prism is a prism that has triangular bases. The diagram

below shows that the volume of a triangular prism is also the product

of the area of the base B and the height h of the prism.

The base B is a triangle.

So, its area is found by

using _^12 bh.

height of prism

height of triangle

Volume of a Triangular Prism

Words The volume V of a triangular

prism is the area of the base B

times the height h.

Model

h

B

Symbols V = Bh, where B is the area of the

base.

Volume of a Triangular Prism

Find the volume of the triangular prism shown.

The area of the triangle is _ 21 · 6 · 8, so

8 ft

6 ft

9 ft

replace B with _^12 · 6 · 8.

V = Bh Volume of a prism

V = (^) ( 12 · 6 · (^8) ) h Replace B with ^12 · 6 · 8.
V = ( ^12 · 6 · (^8) ) 9 The height of the prism is 9.
V = 216 Multiply.
The volume is 216 cubic feet or 216 ft^3.
Find the volume of each triangular prism.
c. 7 in.
4 in.
5 in.
d.
3 mm
5.2 mm
6 mm
Height Do not confuse
the height of the
triangular base with the
height of the prism.
Base Base Before finding the
volume of a prism, identify
the base. In Example 3, the
base is a triangle, so you
replace B with 21 bh.
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