Surface Area of a Pyramid

Today we spent some time looking at the surface areas of pyramids. We already have the skills required to find the surface area of these shapes, but I will go through an example to re-enforce the ideas.
Firstly, we need to remember that the pyramids we look at are all square pyramids. This means that the base is a square, and all 4 of the triangular faces are identical.

Before we look at an example, we should familiarise ourselves with some terms we use when talking about pyramids. The following image shows the parts of the pyramid that we need to know about:

Now when we are looking at finding the surface area, we need to find the area of the 4 identical triangular faces as well as the area of the square base. The area of a triangle is:

The "b" stands for the base length, and the "h" stands for the height of the triangle. Now for these triangular faces, the base length will be the length of one of the sides of the square base. The height of each triangle will be the slant height. 

So now, looking at an example, if we needed to find the surface area of the following pyramid; 

So to find the area of the triangular faces of this, we need the base length and the slant height. We know the base length (10cm), but we don't know the slant height. We can find this using Pythagoras' Theorem. We can make a right angled triangle using the height of the pyramid and half the base length, and use this to find the slant height. The triangle would look like so; 

Now the base of this triangle is 5cm because we are only using half of the 10cm base length to make this triangle. 

To find the slant height, we use Pythagoras' Theorem like so; 

So we now know that the slant height is 13cm. We can use this to find the area of the triangular faces of the pyramid. 

We would do this like so; 

Now we cannot forget about the square base piece either. We would find the area of this like so; 

Now the total surface area is found by adding these two areas together, giving us;

Total Surface Area = 260 + 100

Total Surface Area = 360 cm squared

Using this example, you should be able to work through the surface area of a pyramid problems on the worksheet. This worksheet can be found in the "Work Sheets" tab. 

As always, if you have any questions feel free to comment on this post, or email or chat to me in person.