Calculate Sides and Areas of Similar Shapes Using Area Scale Factors

In this activity, we are going to be looking at the area scale factor of similar shapes. 

What can we remember about scale factors?

A similar shape has the same size angles, but the sides are proportionally bigger or smaller.

We use scale factor to help us to work out any missing lengths.

For example, the squares below have sides of 2 cm and 6 cm.

Therefore, the sides are 6/2 = 3 times bigger on the green one.

This means that all the sides are 3 times bigger.

We call this the scale factor or sf.

So, the scale factor is 3.

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Area scale factor

This is best illustrated in a diagram:

We can see that the squares above have corresponding sides 1 cm and 2 cm so the scale factor is 2.

The area is however 4 times bigger!

In short, if we have the scale factor, we can square it to get the area scale factor!

Let's look at a question to help us understand it.

Example

Two similar shapes have a scale factor of 3.

What is the area scale factor?

Answer

As we said above, we can square the scale factor to get the area scale factor!

Area scale factor = 3² = 9

You can see from the diagram above that the area of the bigger shape is 9 if the scale factor is 3.

Let's try some questions now.