Area of rectangles
Theory
The area of a rectangle is the number of unit squares that cover it. Multiply \(\text{length} \times \text{width}\) and write the answer in square units such as \(\text{cm}^2\) or \(\text{m}^2\).
Area is the amount of surface a shape covers. It is measured in square units such as \(\text{cm}^2\) (square centimetres) or \(\text{m}^2\) (square metres).
A rectangle can be covered exactly by equal rows of unit squares, so its area is the number of those squares.
Instead of counting, multiply: \(\text{Area} = \text{length} \times \text{width}\). The two sides must be in the same unit, and the answer is always a square unit.
The unit of area is a square unit, matched to the unit of the sides.
| Side unit | Area unit | Meaning |
|---|---|---|
| mm | \(\text{mm}^2\) | a \(1\,\text{mm}\) square |
| cm | \(\text{cm}^2\) | a \(1\,\text{cm}\) square |
| m | \(\text{m}^2\) | a \(1\,\text{m}\) square |
How to find the area of a rectangle
- Read the two sides, the length and the width, in the same unit.
- Multiply the length by the width.
- Write the answer in square units that match the sides, such as \(\text{cm}^2\).
| \(3 \times 4\) | \(=\) | \(12\,\text{cm}^2\) |
| \(6 \times 4\) | \(=\) | \(24\,\text{cm}^2\) |
| \(9 \times 7\) | \(=\) | \(63\,\text{m}^2\) |
| \(5 \times 5\) | \(=\) | \(25\,\text{cm}^2\) |
Common pitfalls
Frequently asked questions
How do you find the area of a rectangle?
Multiply the length by the width. A rectangle \(6\,\text{cm}\) by \(4\,\text{cm}\) has area \(6 \times 4 = 24\,\text{cm}^2\).
What is the difference between area and perimeter?
Area is the surface a shape covers, found by multiplying the sides. Perimeter is the distance around the edge, found by adding the sides.
Why is area measured in square units?
Area counts unit squares. Each square has sides of one unit, so a rectangle with centimetre sides is covered by squares of \(1\,\text{cm}^2\).
What is the area of a square?
A square is a rectangle with equal sides, so multiply a side by itself. A square with sides of \(5\,\text{cm}\) has area \(5 \times 5 = 25\,\text{cm}^2\).
Does it matter which side is the length?
No. \(6 \times 4\) and \(4 \times 6\) give the same answer, so it does not matter which side you call the length.