Perimeter
Calculate the perimeter of polygons and composite shapes, and find a missing side given the perimeter.
Worked examples
Perimeter of a rectangle
Straightforward
Problem
Find the perimeter of a rectangle with length cm and width cm.
1
Recall the perimeter formula for a rectangle.
2
Substitute the known values.
3
Add the values inside the brackets.
4
Multiply to find the perimeter.
Answer
cm
Perimeter of a composite shape
Moderate
Problem
A composite L-shaped figure has sides measuring m, m, m, m, m and m. Find the perimeter.
1
The perimeter of any shape is the total distance around the outside. List all the side lengths.
m, m, m, m, m, m
2
Add all the side lengths together.
3
Calculate the sum.
Answer
m
Finding a missing side given perimeter
Challenging
Problem
A rectangle has a perimeter of cm. Its length is cm more than its width. Find the width.
1
Define the unknown. Let the width be cm. Write an expression for the length.
Width cm, Length cm
2
Write the perimeter formula and substitute.
3
Simplify inside the brackets.
4
Expand the brackets.
5
Subtract from both sides.
6
Divide both sides by .
Answer
Width cm, length cm
Practise
Q1·Straightforward
Find the perimeter of a rectangle with length cm and width cm.
Explanation
A rectangle has two pairs of equal sides:
Q2·Straightforward
Find the perimeter of a square with side length m.
Explanation
All four sides are equal:
Q3·Straightforward
A triangle has sides measuring cm, cm and cm. Find its perimeter.
Explanation
Add all three sides:
Q4·Straightforward
A regular hexagon has a side length of cm. Find its perimeter.
Explanation
A regular hexagon has 6 equal sides:
Q5·Moderate
A composite L-shaped figure has sides measuring m, m, m, m, m and m. Find its perimeter.
Explanation
Add all six side lengths:
Q6·Moderate
A composite figure has sides measuring cm, cm, cm, cm, cm and cm. Find its perimeter.
Explanation
Add all six side lengths:
Q7·Moderate
A composite L-shaped figure has sides measuring m, m, m, m, m and m. Find its perimeter.
Explanation
Add all six side lengths:
Q8·Moderate
A composite figure has sides measuring cm, cm, cm, cm, cm and cm. Find its perimeter.
Explanation
Add all six side lengths:
Q9·Challenging
The perimeter of a rectangle is cm and its width is cm. Find the length.
Explanation
Substitute into the perimeter formula:
Q10·Challenging
A regular octagon has a perimeter of m. Find the length of one side.
Explanation
A regular octagon has 8 equal sides, so:
Q11·Challenging
A triangle has a perimeter of cm. Two of its sides measure cm and cm. Find the length of the third side.
Explanation
The third side equals the perimeter minus the two known sides:
Q12·Challenging
A rectangle has a perimeter of m. Its length is m more than its width. Find the width.
Explanation
Let the width be m, so the length is m.