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Hi! I'm Miss Davies! In this lesson we're going to be calculating the volume and surface area of a pyramid.

This is a square based pyramid.

To calculate the volume of a pyramid you need to multiply one-third by the area of the base and multiply it by the height.

As this is a square based pyramid the area of the base is eight squared.

The height of this pyramid is 12 centimetres.

This gives us one-third multiplied by 768, which is 256 centimetres cubed.

Next we're going to calculate the surface area of this pyramid.

It is made up of four isosceles triangles.

We know that they each have a base of eight centimetres and other lengths of 15 centimetres.

In order to work out the area we need to calculate the height.

To do this we're going to use Pythagoras' theorem, by splitting the isosceles triangle into two congruent right angled triangles with a base of four centimetres.

The height of these triangles is 14.

4568 centimetres.

In order to find the area of each of the triangles we're going to use the more accurate version of that answer, which is the square root of 209.

The area of each of the isosceles triangles is 57.

827 centimetres squared.

Next we're going to work out the area of the base, which is a square.

This is 64 centimetres squared.

To find the total surface area of a square based pyramid we need to add together the area of each of the faces.

This is 64, add four lots of 57.

827.

This gives us a total surface area of 295.

3 centimetres squared.

Here are some questions for you to try.

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

Here are the answers.

The height of the triangles is three root 15, or 11.

6 centimetres.

This means that the area of each triangle is 34.

8 centimetres squared.

Here is a question for you to try.

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

Here is the answer.

To calculate the volume of the triangular based pyramid you're going to calculate one-third multiplied by 21 multiplied by 12.

This gives an answer of 84 centimetres cubed.

Here is a question for you to try.

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

Here is the answer.

Because this is a rectangular based pyramid the front and back triangles are the same and the side triangles are the same.

To calculate the height of the front and back triangles you're going to find the square root of three squared, add 25 squared.

This gives an answer of 25.

17 centimetres.

To calculate the height of the side triangles you're going to find the square root of four squared, add 25 squared.

This gives a height of 25.

31 centimetres.

You can then work out the areas.

The front and back triangles have a combined area of 201 centimetres squared.

The side triangles have a combined area of 151 centimetres squared.

And the base has an area of 48 centimetres squared.

I've rounded all of those numbers to the nearest integer.

If you're using the exact values you get an area for the total surface area of 401 centimetres squared.

That's all for this lesson.

Thanks for watching.