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Year 4 Maths Length & Perimeter

Calculate perimeter

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Theory

Perimeter is the total distance all the way around the outside of a shape. This Year 4 measurement page shows how to calculate perimeter by adding all the side lengths, use the square and rectangle shortcuts, work out the perimeter of L-shaped composite shapes, and solve fencing and framing problems in centimetres and metres. Curriculum: VC2M4M02 / AC9M4M02.

The perimeter of a shape is the total distance all the way around its outside. You find it by adding the lengths of all the sides, going right around the shape.

A perimeter is a length, so it is measured in centimetres (cm) or metres (m). Keep the same unit all the way around, and always write the unit in your answer.

Some shapes have a quick way to add. A square has four equal sides, so its perimeter is 4 times one side. A rectangle has equal opposite sides, so you can add the length and the width and then double the total. Perimeter is not the same as area, which is the space inside the shape.

Rectangle 7 cm by 4 cm with the perimeter highlighted A rectangle 7 cm long and 4 cm wide. The outline is highlighted in red to show the perimeter, which is 7 plus 4 plus 7 plus 4, equal to 22 cm. 7 cm 7 cm 4 cm 4 cm
The perimeter is the red outline: 7 + 4 + 7 + 4 = 22 cm.
L-shaped composite shape with every side labelled An L-shaped shape with sides 6 cm, 6 cm, 2 cm, 3 cm, 4 cm and 3 cm. The outline is highlighted in red. The perimeter is 6 plus 6 plus 2 plus 3 plus 4 plus 3, equal to 24 cm. 6 cm 6 cm 2 cm 3 cm 4 cm 3 cm
Add every side of an L-shape: 6 + 6 + 2 + 3 + 4 + 3 = 24 cm.

These perimeter facts help you find the distance around a shape. The main rule works for every shape; the square and rectangle rules are quick shortcuts.

\[ \text{Perimeter} = \text{add all the side lengths} \]
Perimeter=add all the side lengths
\[ \text{Square: } \text{Perimeter} = 4 \times \text{side} \]
Perimeter=4×side
\[ \text{Equilateral triangle: } \text{Perimeter} = 3 \times \text{side} \]
Equilateral triangle: Perimeter=3×side
\[ \text{Rectangle: } \text{Perimeter} = \text{length} + \text{width} + \text{length} + \text{width} \]
Perimeter=length+width+length+width
Rectangle shortcut. Because opposite sides are equal, add the length and the width first, then double it. For a rectangle 7 cm by 4 cm: \(7 + 4 = 11\), then \(11 + 11 = 22\) cm.

How to calculate a perimeter

  1. Find every side. Look around the outside of the shape and note each side length. Check they are all in the same unit.
  2. Add them up. Add all the side lengths together, going right around the shape so no side is missed.
  3. Write the unit. Give the answer with cm or m.

Working backwards and real problems

  1. Missing side of a square or equilateral triangle. Divide the perimeter by the number of equal sides (\(4\) or \(3\)).
  2. Missing width of a rectangle. Take the two lengths away from the perimeter, then halve what is left.
  3. Fences, frames and laps. These are perimeters. Take off any gap such as a gate. If fencing comes in rolls, divide the total length by the length of one roll.
Example 1 — Triangle
A triangle has sides of 7 cm, 9 cm and 6 cm. Work out its perimeter.
Triangle with sides 7 cm, 9 cm and 6 cm A triangle with a base of 9 cm, a left side of 6 cm and a right side of 7 cm. The perimeter is 7 plus 9 plus 6, equal to 22 cm. 9 cm 6 cm 7 cm
Solution
\(\text{Perimeter}\)\(=\)\(7 + 9 + 6\)
\(\text{Perimeter}\)\(=\)\(22 \text{ cm}\)
7+9+6=22

The perimeter is 22 cm.

Example 2 — Rectangle
A rectangle is 9 cm long and 5 cm wide. Work out its perimeter.
Rectangle 9 cm long and 5 cm wide A rectangle 9 cm long and 5 cm wide. The perimeter is 9 plus 5 plus 9 plus 5, equal to 28 cm. 9 cm 9 cm 5 cm 5 cm
Solution
\(\text{length} + \text{width}\)\(=\)\(9 + 5 = 14\)
\(\text{double it}\)\(=\)\(14 + 14 = 28 \text{ cm}\)
9+5+9+5=28

The perimeter is 28 cm.

Example 3 — Find a side
A square has a perimeter of 36 cm. How long is one side?
Square with a perimeter of 36 cm and an unknown side A square with a perimeter of 36 cm. One side is marked with a question mark. Because the four sides are equal, one side is 36 divided by 4, equal to 9 cm. ? cm P = 36 cm
Solution
\(\text{one side}\)\(=\)\(36 \div 4\)
\(\text{one side}\)\(=\)\(9 \text{ cm}\)
36÷4=9

Each side is 9 cm.

Example 4 — L-shaped garden
A garden bed is the L-shape shown. Work out the perimeter.
L-shaped garden bed with sides 8 m, 2 m, 5 m, 3 m, 3 m and 5 m An L-shaped garden bed. The sides are 8 m, 2 m, 5 m, 3 m, 3 m and 5 m. The perimeter is 8 plus 2 plus 5 plus 3 plus 3 plus 5, equal to 26 m. 8 m 2 m 5 m 3 m 3 m 5 m
Solution
\(\text{Perimeter}\)\(=\)\(8 + 2 + 5 + 3 + 3 + 5\)
\(\text{Perimeter}\)\(=\)\(26 \text{ m}\)
8+2+5+3+3+5=26

The perimeter is 26 m. Do not forget the two step sides.

Example 5 — Equilateral triangle
An equilateral triangle has three equal sides.
(i) Its sides are \(8\) cm. Find the perimeter.
(ii) Another one has a perimeter of \(27\) cm. How long is one side?
Solution
\(\text{(i) } 3 \times 8\)\(=\)\(24\text{ cm}\)
\(\text{(ii) } 27 \div 3\)\(=\)\(9\text{ cm}\)
3 x 8 = 24 cm; 27 / 3 = 9 cm

Three equal sides: multiply one side by \(3\). To go back from the perimeter, divide by \(3\).

Example 6 — Missing width
A rectangle has a perimeter of \(34\) cm. Its length is \(11\) cm. How wide is it?
Solution
\(\text{two long sides}\)\(=\)\(11 + 11 = 22\text{ cm}\)
\(\text{two short sides}\)\(=\)\(34 - 22 = 12\text{ cm}\)
\(\text{width}\)\(=\)\(12 \div 2 = 6\text{ cm}\)
34 - 22 = 12, 12 / 2 = 6 cm

Take the two long sides away from the perimeter. What is left is shared by the two short sides. The width is \(6\) cm.

Example 7 — Fence with a gate
A paddock is a rectangle \(30\) m long and \(20\) m wide. The fence goes all the way around except a \(4\) m gate.
(i) Find the perimeter.
(ii) How much fencing is needed?
(iii) Fencing comes in \(8\) m rolls. How many rolls are needed?
Solution
\(\text{(i) } 30 + 20 + 30 + 20\)\(=\)\(100\text{ m}\)
\(\text{(ii) } 100 - 4\)\(=\)\(96\text{ m}\)
\(\text{(iii) } 96 \div 8\)\(=\)\(12\text{ rolls}\)
100 m, 100 - 4 = 96 m, 96 / 8 = 12 rolls

The gate is a gap, so take it off the perimeter. \(12\) rolls of \(8\) m give exactly \(96\) m.

Example 8 — Which perimeter is bigger?
A square has sides of \(9\) cm. A rectangle is \(15\) cm long and \(2\) cm wide. Which has the larger perimeter?
Solution
\(\text{square}\)\(=\)\(4 \times 9 = 36\text{ cm}\)
\(\text{rectangle}\)\(=\)\(15 + 2 + 15 + 2 = 34\text{ cm}\)
\(36\)\(>\)\(34\)
square 36 cm, rectangle 34 cm

Work out both perimeters, then compare. The square has the larger perimeter, even though the rectangle is longer.

Example 9 — A frame in metres
A square mirror has sides of \(35\) cm. How much wood is needed to frame all four sides? Write it in centimetres, then in metres and centimetres.
Solution
\(4 \times 35\)\(=\)\(140\text{ cm}\)
\(140\text{ cm}\)\(=\)\(100\text{ cm} + 40\text{ cm}\)
\(140\text{ cm}\)\(=\)\(1\text{ m }40\text{ cm}\)
4 x 35 = 140 cm = 1 m 40 cm

A frame goes around the outside, so it is the perimeter: \(140\) cm, or \(1\) m \(40\) cm.

Common pitfalls

Perimeter is not area. Watch out for multiplying the length by the width. That gives the area (the space inside). For perimeter, add the sides that go around the outside.
Length plus width is only half. For a rectangle \(6\) m by \(3\) m, \(6 + 3 = 9\) m covers only two sides. The perimeter is \(9 + 9 = 18\) m.
Do not miss a side. On an L-shape or other composite shape, add every side, including the short step sides where the shape bends in. Miss one and the perimeter is too small.
Keep the units the same. Do not mix centimetres and metres, and always write cm or m in the answer.

Frequently asked questions

What is the perimeter of a shape?

The perimeter is the total distance all the way around the outside of a shape. You find it by adding the lengths of all the sides.

How do you work out the perimeter of a rectangle?

Add all four sides. Because opposite sides are equal, you can add the length and the width and then double the total. A rectangle 7 cm by 4 cm has a perimeter of \(7 + 4 + 7 + 4 = 22\) cm.

What is the difference between perimeter and area?

Perimeter is the distance around the outside of a shape and is measured in cm or m. Area is the amount of space inside the shape and is measured in square units. For perimeter you add the sides; for area you do not.

How do you find the perimeter of a square?

A square has four equal sides, so multiply the length of one side by 4. A square with sides of 11 cm has a perimeter of \(4 \times 11 = 44\) cm.

How do you find the perimeter of an L-shape?

Add every side, going right around the shape. Do not forget the short step sides where the shape bends in. Miss a side and the perimeter will be too small.

If a square has a perimeter of 32 cm, how long is one side?

Divide the perimeter by 4, because the four sides are equal. \(32 \div 4 = 8\), so one side is 8 cm.

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