Calculate Lengths of Sides in Similar Shapes Using Scale Factors

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?