Calculate the Scale Factor of Similar Shapes

In this worksheet, students will identify similar shapes and calculate the scale factor

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Use Scale Factors/Diagrams and Maps

Difficulty level:

Worksheet Overview

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 90o, but the sides are all different lengths.

To see how many times bigger or smaller the shapes are we use scale factor.

Example

The rectangles are mathematically similar.

We can compare the sides by counting the squares

If we look at the base lengths, we can see that the bigger one is 4 and the smaller one is 2.

These are called corresponding sides because they are the equivalent side on the new shape.

To find out how many times bigger the big shape is we can divide the bigger base by the smaller:

4 ÷ 2 = 2

This means that the bigger rectangle has sides which are twice as long as the small one.

We call this the scale factor (or sf. for short)

So, the scale factor is 2

In this case, we have another pair of corresponding sides (the height).

So, we can check the scale factor, as it should be the same.

If not, then the shapes are not similar!

Heights are 6 and 3

6 ÷ 3 = 2

The shape is similar and the scale factor is 2.

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