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Same Area - Different Perimeter

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

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'Same Area - Different Perimeter' worksheet

Key stage:  KS 2

Year:  Year 4 11+ worksheets

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:

 

           
           
           
           
           
           


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

 

The 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.

 

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

 

           
           
           
           
           
           


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

 

The 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 2 + 1 + 1 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 = 14 cm.

 

Shapes with the same area can have different perimeters.

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