# Word Problem Involving the Volume of a Triangular Prism

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In this lesson, we solve word problems involving the volume of a triangular prism. Real world problems.

A right prism base is a triangle whose sides are 18 cm, 20 cm and 34 cm. Find the volume of the prism if its height is 9 cm.

### Solution

Step 1:

Area of baseA = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{36(36-18)(36-20)(36-34)}$

= 144 square cm;

height h = 9 cm

Step 2:

Volume of triangular prism V = Ah = 144(9)

= 1296 cu cm

The base of a right prism is a right triangle with legs 12 and 5 cm. If the volume of the prism be 390 cu cm, find the height of the prism.

### Solution

Step 1:

Area base A = $\frac{1}{2}$ × 12 × 5 = 30 sq cm;

Volume V = 390 cu cm

Step 2:

Height of triangular prism h = V/A = 390/30

= 13 cm