Compound shapes

Sometimes shapes can be more complicated. Be particularly careful to add up the lengths of every side when you work out the total perimeter.

Perimeter of a compound shape diagram

Perimeter = 2 + 2 + 3 + 3 + 5 + 5 = 20~cm

In some cases you’ll need to calculate the 'missing' lengths, eg x and y in the question below.

Question

A plan of a play area is shown below:

Perimeter of a compound shape diagram

a) Calculate the length of x and y.

b) Calculate the perimeter of the play area.

a) The length of the play area is 20~m, so x = 20 - 8 = 12~m.

The width of the play area is 15~m, so y = 15 - 5 = 10~m.

b) Perimeter = 8 + 5 + 12 + 10 + 20 + 15 = 70~m.

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