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Same Perimeter - Different Area

In this worksheet, students must recognise that shapes with the same perimeters can have different areas.

'Same Perimeter - Different Area' worksheet

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Perimeter and Area

Difficulty level:  

Worksheet Overview

Look at the red shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

Its perimeter is the total of the distances around all four sides.

Starting at the base and going anticlockwise around the shape, we work out that:

the perimeter is 2 + 3 + 2 + 3 = 10 cm.

 

It is made of 6 centimetre squares, so its area is 6 cm2.

 

Now look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           



Its perimeter is the total of the distances around all its sides.

Starting at the base and going anticlockwise around the shape, we work out that:

the perimeter is 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 = 10 cm.

This is the same perimeter as the red shape above.

 

But it is only made of 4 centimetre squares, so its area is only 4 cm2.

 

Shapes with the same perimeter can have different areas.

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