Lesson video

Hi, I'm Miss Davis.

And in this lesson, we're going to be working out the volume of triangular prisms. Here we have a triangular prism.

If a triangular prism has the end two faces are two identical triangles.

If we cut through this prism, parallel to the two triangles, the cut will always look the same.

To find the volume of this triangular prism, we need to find the area of the cross-section which is the triangle, and multiply it by the length.

We can write this as width multiplied by height multiplied by length divided by two.

If we substitute in the values from this example, we have 10, multiplied by eight, multiplied by seven divided by two.

This is the same, is 560 divided by two or 280 centimetres cubed.

In this next example, we don't have a right-angled triangle, and we have two lengths that could be considered as the height.

Let's start by writing down our formula.

Width multiplied by height multiplied by length divided by two, as it is a triangular prism.

The width of the prism is 12 metres and the length is 20 metres.

But is the height five or nine? It is five, as that is the height that goes straight up perpendicular to the base.

This means it meets the base at a right angle.

I've substituted these values into our formula to get 12 multiply by five, multiplied by 20 divided by two.

This is the same as 1,200 divided by two.

The volume of this triangular prism is 600 metres cubed.

Here are some questions for you to try.

Pause the video to complete your task and resume once you finished.

Here are the answers.

Make sure that you're dividing by two after multiplying together the width, height, and length.

For part D, the 12.

5 millimetres isn't needed.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

Both Tom and Lisa are correct because multiplication is commutative.

This means that we can do the calculations in any order.

In this next example, we've been told that the triangular prism and the cuboid have the same volume.

Let's start by working out the volume of the cuboid.

This is found by multiplying the length by the width by the height.

In this case, five times 12 times 20.

This gives a volume of 1,200 centimetres cubed.

This is also the volume of the triangular prism.

We can write this as 1,200 is equal to 12 multiplied by 25, multiplied by y, divided by two.

This is the same as 1,200 is equal to 300y, or 300 times y divided by two.

The first thing we're going to do to start solving this equation is multiply both sides by two.

This gives us 2,400 is equal to 300y.

To work out y, we're going to divide both sides by 300.

This gives an answer of y equals eight centimetres.

Here's a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The volume of the cuboid is 180 centimetres cubed.

To find x, we need to multiply this by two, and then divide by nine and eight to get the answer of x equals five centimetres.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The volume of the triangular prism is 729 centimetres cubed.

To find the length of the cube, we need to find the cubed root of 729.

This is nine.

So x is nine centimetres.

Here's a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here's the answer.

The volume of the triangular prism is 450 centimetres cubed.

To find the mass of an object, you should multiply the volume by the density, in this case, 450 to get multiplied by 1.

3.

This gives an answer of 585 grammes.

That's all for this lesson.

Thanks for watching.