In this activity, we are going to be looking at **similar **shapes and **scale factor**.

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

For example, the squares below are all similar because they have the same angles of 90^{o} but the sides are all different lengths.

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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Let's have a look at a typical question.

**Question**

Below are two mathematically similar rectangles. Find the missing side** a.**

**Answer**

**Step 1** - We need to know the scale factor.

Find two corresponding sides: 6 cm and 3 cm

The scale factor is 6 ÷ 3 = 2 (so, each side on the big one is twice as long as the small one)

So,** the scale factor is 2.**

**Step 2 **- We use the scale factor to find the missing side.

a = 1 cm x scale factor of 2.

1 x 2 = 2 cm

**a = 2 cm**

Are you ready to have a go?