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# Volumes of triangular shaped prisms. How to work out the volume of a triangular prism.

Working out the volume of a triangular prism is basically a two step problem:

First you will need to calculate the cross-sectional area of the triangular prism (area of the triangle at the front of the shape). To find the area of a triangle multiply the base by the height and halve the answer (A = 1/2bh).

Secondly, multiply the cross-sectional area by the length of the prism.

So to summarise, **find the area of the triangle and multiply by the length.**

So let’s take a look at some examples of working out the volume of a triangular prism:

**Example 1**

Work out the volume of this triangular prism.

The base of the triangle is 18 inches and height is 7 inches, therefore, the cross-sectional area of the triangular prism is:

½ × 18 × 7 (since the area of a triangle can be found using A = 1/2bh)

= 63 inches²

Now since you have the cross-sectional area, you can now multiply this answer by the length to give the volume of the prism:

Volume = 63 × 25 = 1575 inches³

**Example 2**

A water trough in the shape of a triangular prism is filled with water. Work out how many litres of water the trough can hold.

First you need to work out the volume of the triangular prism in cm³.

The base of the triangle is 50 cm and height is 40 cm, therefore, the cross-sectional area of the triangular prism is:

½ × 50 × 40 (since the area of a triangle can be found using A = 1/2bh)

= 1000 cm²

Now since you have the cross-sectional area, you can now multiply this answer by the length to give the volume of the prism. Make sure you convert the 1.8m into cm first by multiplying 1.8 by 100 as there are 100cm in 1m:

1.8m = 1.8× 100 = 180cm

So the volume is:

Volume = 1000 × 180 = 180,000 cm³

All you need to do now is convert the 180,000 cm³ into litres.

Now, 1000 cm³ of water is the same as 1 litre of water. So all you need to do now, is divide the 180,000 cm³ by 1000:

180,000 ÷ 1000 = 180 litres.

So you can fill the trough with 180 litres of water.

So just to recap, the volume of a triangular of prism can be found by working out the cross-sectional area and multiplying the answer by the length.