Calculate perimeter - Rectangles & squares
Theory
The perimeter is the total distance around the outside of a shape. A rectangle has two lengths and two widths, so its perimeter is \(2 \times (\text{length} + \text{width})\); a square has four equal sides, so its perimeter is \(4 \times \text{side}\). This Year 5 maths page shows how to use these rules, how to work backwards from a perimeter to a side, and how to solve fencing problems.
The perimeter of a shape is the total length of its boundary. It is measured in units of length, such as cm or m.
Opposite sides of a rectangle are equal. If only one length and one width are marked, the other two sides are the same.
Rectangle: \(P = l + w + l + w = 2 \times (l + w)\). Square with side \(s\): \(P = 4 \times s\).
Working backwards: half the perimeter of a rectangle is one length plus one width. For a square, the side is the perimeter divided by \(4\).
Perimeter rules:
Perimeter of a rectangle
- Add the length and the width.
- Double the result.
Missing side from the perimeter
- Halve the perimeter to get one length plus one width.
- Subtract the side you know.
- For a square, divide the perimeter by \(4\).
| \(2 \times (11 + 6)\) | \(=\) | \(34\text{ cm}\) |
\(34\) cm.
| \(4 \times 7\) | \(=\) | \(28\text{ cm}\) |
\(28\) cm.
(i) How long is the side opposite the \(14\) cm side?
(ii) What is the perimeter?
| \(2 \times (14 + 5)\) | \(=\) | \(38\text{ cm}\) |
(i) \(14\) cm
(ii) \(38\) cm
| \(64 \div 4\) | \(=\) | \(16\text{ m}\) |
\(16\) m.
| \(36 \div 2\) | \(=\) | \(18\) |
| \(18 - 10\) | \(=\) | \(8\text{ cm}\) |
The width is \(8\) cm.
| \(2 \times (30 + 22)\) | \(=\) | \(104\text{ m}\) |
\(104\) m of fencing.
| \(2 \times (10 + 8)\) | \(=\) | \(36\) |
| \(4 \times 9\) | \(=\) | \(36\) |
Both are \(36\) cm, even though the shapes are different.
| \(2 \times (16 + 9)\) | \(=\) | \(50\text{ m}\) |
She added only two of the four sides. The perimeter is \(50\) m.
Common pitfalls
Frequently asked questions
What is perimeter?
The total distance around the outside of a shape.
How do you find the perimeter of a rectangle?
Add the length and width, then double: \(2 \times (11 + 6) = 34\) cm.
How do you find the perimeter of a square?
Multiply one side by \(4\): \(4 \times 7 = 28\) cm.
How do you find the side of a square from its perimeter?
Divide the perimeter by \(4\): \(64 \div 4 = 16\) m.
Can different shapes have the same perimeter?
Yes. A \(10\) by \(8\) rectangle and a square with sides of \(9\) both have a perimeter of \(36\).