Recognize that shapes with the same areas can have different perimeters and vice versa

Introduced in the Year 6 curriculum as: "Recognise that shapes with the same areas can have different perimeters and vice versa"

It is not always the case that shapes with the same area have the same perimeter. Likewise, it is not always true that shapes with the same perimeter have equal area.


Example 1:

Look at these two shapes:

A B

Are their perimeters equal?

A: 3 + 6 + 5 + 2 + 8 + 8 = 32

B: 10 + 2 + 4 + 4 + 2 + 4 + 4 + 2 = 32

They each have a perimeter of 32cm.

Do they have the same area?

No! The area of shape A is (6 x 3) + (2 x 8) = 34cm².

The area of shape B is (2 x 10) + (4 x 2) = 28 cm².


Example 2:

The two shapes below have the same area:

They both have an area of 6 squares.

Do they have the same length perimeter?

Each shape is made up of 4 straight lines along the grid and 4 diagonal lines across the grid.

Yes! They have both equal area and equal perimeter.


Example 3:

These shapes have different perimeters:

E F

E has a perimeter of 34cm, F has a perimeter of 32cm.

Does this mean that their areas are different?

Not always! The area and perimeter of two shapes can be the same or different.

We need to calculate the area of each shape.

E: (10 x 4) + (4 x 3) = 40 + 12 = 52cm²

F: (6 x 6) + (4 x 4) = 36 + 16 = 52cm²

The areas are the same. They are both 52cm².


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