VOLUME OF TRIANGULAR PRISM

In a 3-D figure, if the base is a rectangle or square, two of the side walls side walls are triangles and other two side walls are rectangles or squares, then the 3-D figure is called triangular prism.

Any triangular prism will look like the one shown below.

The formula to find volume of the above triangular prism is

= (1/2) x Base Area x Height

Important Note :

The above formula will work only if the given figure meets the following conditions.

(i) The base must be a rectangle or square.

(ii) Two of the side walls side walls must be triangles.

(iii) Other two side walls must be rectangles or squares.

Example 1 :

Find the volume of the prism.

Solution :

Step 1 :

In the given prism, the base is  a rectangle, two of the side walls are triangles and other two side walls are rectangles.

So, the given prism is a triangular prism.

Step 2 :

Volume of a triangular prism = (1/2) x base area x height

V = (1/2) x B x h

Step 3 :

Find base area

Base Area = l x w

22 x 24

= 528 sq.m

Step 4 :

Find volume of the triangular prism

V = (1/2) x b x h

= (1/2) x (528) x 7

= 1848 cubic meters 

Example 2 :

Bradley’s tent is in the shape of a triangular prism shown below. How many cubic feet of space are in his tent ?

Solution :

Step 1 :

To find the number of cubic feet of space in Bradley’s  tent, we have to find the volume of his tent.

Step 2 :

Volume of a triangular prism = (1/2) x base area x height

V = (1/2) x b x h

Step 3 :

Find base area.

Base Area = l x w

= 9 x 6

= 54 sq.ft

Step 4 :

Find volume of the triangular prism.

V = (1/2) x b x h

= (1/2) x (54) x 4

= 108 cubic feet

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