In this activity, we are using ratio to find scale factors and missing lengths.

**Similar shapes have matching corresponding angles and corresponding sides which are in the same ratio.**

We can look at corresponding sides of similar shapes to get the scale factor.

Scale factor is how many times longer the sides are from one shape to another.

The regular pentagons below have corresponding sides of 4 cm and 8 cm.

As a ratio we would write 4 : 8

This can be simplified by dividing both by 4

Simplified ratio is 1 : 2

This means that the sides on the larger pentagon are 2 times longer than the smaller one.

We call this the **scale factor!**

Let's look at a typical question!

__Example__

The rectangles below are similar.

Calculate the __area__ of rectangle B.

**Answer**

The ratio of the bases is 2:6

Simplifies to 1:3 by dividing by 2

This means the sides of B are 3 times longer than A

To find the missing side we know it is 3 times longer than its corresponding side (4)

The missing side = 3 x 4 = 12 cm

Not quite finished!

We now have to find the area of B = base x height

**Area of B = 6 x 12 = 72 cm ^{2}**

Let's have a go at the questions now.