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 = 3 ^{2} = 9**

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

Does that make sense?