Understand Shapes With the Same Area but Different Perimeter

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.

Shapes with the same area can have different perimeters.

You will need to use this knowledge to solve a series of questions and solve some problems.