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Hi, I'm Miss Davies, and in this lesson, we're going to be finding the surface area of triangular prisms. This is a right angled triangular prism.

This is the net of this prism.

Imagine all of the faces have been folded down flat.

This is what the result would be.

This net will help us working out the surface area of the triangular prism.

Let's start by labelling all of the sides.

We can now begin to work out the surface area of the triangular prism.

I have colour coded and labelled the different sized faces of the prism.

To find the surface area of the triangular prism, we're going to calculate the area of each face.

Let's start with face A.

The area of face A is found by multiplying seven by six, to give 42 centimetres squared.

Face B is found by multiplying seven by eight.

This gives an area and 56 centimetres squared.

Face C is found by multiplying seven by 10.

So face C has an area of 70 centimetres squared.

To find the area of the faces that are labelled D, we going to multiply six by eight and divide by two.

This gives 24 centimetres squared.

This means that both of the faces that are labelled D have an area of 24 centimetres squared.

To find the total surface area of the triangular prism, we need to add the area of each of the faces together.

This gives 216 centimetres squared.

Here's some questions for you to try.

It might be a good idea to draw out a sketch of the net of each of the triangular prisms. Pause the video to complete your task, and resume once you're finished.

Here are the answers.

Remember the two triangular faces on a triangular prism are identical, so you don't need to work these out separately.

In this next example, we've been asked to calculate the surface area of the isosceles triangular prism.

This means that two of the lengths of the triangular prism are equal.

I have drawn a net.

Because it is an isosceles triangular prism, I know that the faces I've labelled B are equal.

Face A is the base of the prism and faces C are the two triangular ends.

Let's start by working out the area of face A.

This is found by multiplying 24 and 18 together.

This gives 432 centimetres squared.

To find the area of faces B, we're going to multiply 18 by 20.

The area of each of these faces is 360 centimetres squared.

To find the area of the faces labelled C, we're going to multiply 24 by 16 and divide by two.

This gives an area if 192 centimetres squared.

To find the total surface area of this prism, we'd add the area of each of the faces together.

These can be written as 432 add two lots of 360, add two lots of 192.

This gives a total surface area of 1,536 centimetres squared.

Here's some questions for you to try.

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

Here are the answers.

An equilateral triangular prism, will be made up of two identical triangular bases and three identical rectangular faces.

While an isosceles triangular prism is made up of two identical triangular faces, two identical rectangular faces, and one of their rectangular face.

Here's a question for you to try.

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

Here are the answers.

Rory shouldn't have multiplied the base by two, as there is only one of this size rectangle.

In this next example, we've been asked to calculate the surface area of the isosceles triangular prism.

Let's draw out the net to represent this prism.

Why can't we work out the surface area straight away? Well done if you noticed that we're missing these lengths.

To work out these lengths, we're going to have to use Pythagoras's theorem.

We can say that 16 squared, add 12 squared, which is half of 24 is equal to the missing length squared.

It's the same as 256, add 144 is equal to something squared.

This can be simplified to 400 equals something squared.

So our missing length is the square root of 400, which means our missing length is 20 centimetres.

We can then use this to find the total surface area of the triangular prism.

Here's a question for you to try.

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

You needed to use Pythagoras's theorem to calculate the diagonal length on this triangular prism.

You can then use this to help with finding the surface area.

That's all for this lesson, thanks for watching.