Recognise that Shapes with the Same Area can have Different Perimeters

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.

Can you see that shapes with the same area can have different perimeters?

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