Unit 22 Section 6 : Volume of a Triangular Prism

This section looks at how to find the volume of a triangular prism.
You will need to remember how to find the area of a triangle in order to do this:

A triangular prism has the same triangular cross-section throughout its length.


 

Example Question

The diagram below shows a triangular prism:

(a) Calculate the volume of the prism if l = 5 cm.

Volume = area of cross-section × length
             = 10 cm² × 5 cm
             = 50 cm³

The volume is 50 cm³

(b) Calculate the volume of the prism if l = 2 m.

We need all the units to be cm or cm², so we need to convert 2 metres into 200 centimetres.

Volume = area of cross-section × length
             = 10 cm² × 200 cm
             = 2000 cm³

The volume is 2000 cm³
 

Practice Questions

Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

Practice Question 1
Look at the triangular prism below.
(a) What is the area of the end of the prism?

(b) What is the volume of the prism?

Practice Question 2
The triangular prism opposite has a volume of 82 cm³.
The area of the end of the prism is A.

(a) Write down an equation involving A.

(b) Solve your equation to find the area of the end of the prism.

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Calculate the volume of each of the triangular prisms below.
(a) cm³
(b) cm³
(c) cm³
(d) cm³
Question 2
Two identical triangular prisms are stuck together to form a rectangular block.
One prism is shown below:

(a) What is the volume of this prism?
cm³

(b) What is the volume of the rectangular block
formed when the two prisms are stuck together?
cm³

Question 3
A model house is made by sticking a triangular prism on top of a rectangular block, as shown in the diagram.

Calculate the volume of the model house.
cm³

Question 4
The triangular prism shown below has a volume of 84 cm³.

(a) What is the area of the shaded end of the prism?
cm²

(b) If the length was increased to 6 cm, what would be the new volume of the prism?
cm³

Question 5
The volume of this triangular prism is 63 cm³ and the area of the shaded end is 10.5 cm².

Find the length of the prism.
cm

Question 6
The volume of this triangular prism is 42 cm³.

What is the height of the prism?
cm

Question 7
A triangular prism has a triangular hole cut in it.

Calculate the volume of the prism after the hole has been cut out.
cm³


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Produced by A.J.Reynolds May 2011