Calculate Missing Sides in Similar Shapes

Remember, shapes that have the same size angles and are enlargements of each other are called  similar.

 

 

When we enlarge a shape we use a multiplier 

We call it a scale factor

 

The shapes below are similar!   

 

 

We can find the scale factor.

Large height ÷ Small height = 6 ÷ 2 = 3

or

Large base ÷ Small base = 3 ÷ 1 = 3

 

Both answers are 3, so the scale factor is 3

 

We can use this to find any missing sides. Let's try a question.

 

Example

The shapes below are similar.

Work out the length of the missing side, A.

 

 

Answer

To find the scale factor, we can divide the heights because we have both.

Scale factor = 12 ÷ 6 = 2

 

To find base A we can multiply the small base by the scale factor:

5 x 2 = 10

A = 10

 

Let's try some questions like this!