What is the perimeter of a shape?
The perimeter of a shape is the distance around its edge.
Example
An ant walks all the way around the edge of a rectangle, measuring \(3~cm\) by \(4~cm\).
What distance will it have travelled?
Perimeter \(= 4 + 3 + 4 + 3 = 14~cm\)
Key point
When calculating the perimeter, remember to include the length of every side.
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 \(= 2 + 2 + 3 + 3 + 5 + 5 = 20~cm\)
In some cases you’ll need to calculate the 'missing' lengths, eg \(x\) and \(y\), as in the question below.
Question
A plan of a play area is shown:
a) Calculate the length of \(x\) and \(y\).
b) Calculate the perimeter of the play area.
Answer
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 \(= 8 + 5 + 12 + 10 + 20 + 15 = 70~m\).
Test section
Question 1
What is the perimeter of the following rectangle (each square has a side length of \({1}~{cm}\))?
Answer
Add the lengths of each side together. \({2}~{cm}+{5}~{cm}+{2}~{cm}+{5}~{cm}={14}~{cm}\).
Question 2
What is the perimeter of the following shape (each square has a side length of \({1}~{cm}\))?
Answer
Add the lengths of each side together. \({2}~{cm}+{1}~{cm}+{1}~{cm}+{1}~{cm}+{1}~{cm}+{3}~{cm}+{2}~{cm}\) \(+~{3}~{cm}+{1}~{cm}+{1}~{cm}+{1}~{cm}+{1}~{cm}={18}~{cm}\).
Question 3
What is the perimeter of a square whose sides are \({6}~{cm}\)?
Answer
Add the lengths of each side together. \({6}~{cm}+{6}~{cm}+{6}~{cm}+{6}~{cm}={24}~{cm}\).
Question 4
What is the perimeter of a rectangle whose sides are \({10}~{cm}\) and \({2}~{cm}\)?
Answer
Count the distance around the rectangle. \({10}~{cm}+{2}~{cm}+{10}~{cm}+{2}~{cm}={24}~{cm}\).
Question 5
What is the perimeter of a regular hexagon whose sides are \({5}~{cm}\)?
Answer
A regular hexagon has \({6}\) equal sides.
In this case, perimeter \(={6}\times{5}={30}~{cm}\).
Question 6
What is the perimeter of the following shape?
Answer
Count the lengths around the edge of the shape.
\({1}~{cm}+{4}~{cm}+{5}~{cm}+{2}~{cm}+{4}~{cm}+{2}~{cm}={18}~{cm}\).
Question 7
What is the length of \({x}\)?
Answer
Use the given lengths to find the missing lengths.
In this case \({15}~{m}-{4}~{m}={11}~{m}\).
Question 8
What is the length of \({y}\)?
Answer
Use the given length to find the missing length. In this case \({10}~{m}-{2}~{m}={8}~{m}\).
Question 9
What is the perimeter of a right-angled triangle whose short sides are \({3}~{cm}\) and \({4}~{cm}\), and hypotenuse (longest side) is \({5}~{cm}\)?
Answer
You need to add all three sides.
Perimeter of triangle \(={3}~{cm}+{4}~{cm}+{5}~{cm}={12}~{cm}\).
Question 10
What is the perimeter of the following shape?
Answer
Calculate the length of the missing sides before counting the distance around the shape, \({5}~{m}+{2}~{m}+{4}~{m}+{2}~{m}+{5}~{m}\) \(+~{8}~{m}+{14}~{m}+{8}~{m}={48}~{m}\).
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