Area of rectangles using a grid
Theory
Area of rectangles using a grid is a Year 4 measurement skill: finding how many unit squares cover a rectangle. This page shows how to count squares on a centimetre grid, how rows of squares times the squares in each row links to multiplication, and how area is measured in square centimetres and square metres. Curriculum: VC2M4M02 / AC9M4M02.
Area is the amount of surface a shape covers. We measure it in square units. On a 1 cm grid, every small square is one square centimetre, written \(1\text{ cm}^2\).
To find the area of a rectangle on a grid, count the unit squares inside it. The squares sit in equal rows, so instead of counting one by one you can multiply: the number of rows times the number of squares in each row. This is the same as length times width.
A rectangle with 4 rows of 7 squares covers \(4 \times 7 = 28\) squares, so its area is \(28\text{ cm}^2\). On a metre grid each square is \(1\text{ m}^2\), and the counting works the same way.
Finding the area of a rectangle uses one simple rule, written two ways.
How to find the area of a rectangle on a grid
- Count the rows. Look at the rectangle on the grid and count how many rows of squares it has.
- Count each row. Count how many squares are in one row. Every row has the same number.
- Multiply. Times the number of rows by the squares in each row. Write the answer in square units, like \(\text{cm}^2\) or \(\text{m}^2\).
- Check. Counting every square, adding the rows (\(7 + 7 + 7 + 7\)) and multiplying (\(4 \times 7\)) all give the same answer.
If you know the area and one side, work backwards: ask what number times the side gives the area, or divide the area by the side.
| \(9 + 9 + 9\) | \(=\) | \(27\) |
| \(3 \times 9\) | \(=\) | \(27\) |
Adding the rows or multiplying gives the same count. The area is \(27\text{ cm}^2\).
| \(\text{length} \times \text{width}\) | \(=\) | \(9 \times 4\) |
| \(9 \times 4\) | \(=\) | \(36\) |
The area is \(36\text{ cm}^2\).
| \(5\text{ rows of }8\text{ tiles}\) | \(=\) | \(8 \times 5\) |
| \(8 \times 5\) | \(=\) | \(40\) |
The area is \(40\text{ m}^2\). Adding \(8 + 5 = 13\) would not count the tiles.
| \(2 \times 14\) | \(=\) | \(28\text{ cm}^2\) |
| \(4 \times 7\) | \(=\) | \(28\text{ cm}^2\) |
A \(4\text{ cm}\) by \(7\text{ cm}\) rectangle has the same area, \(28\text{ cm}^2\). So does \(1\text{ cm}\) by \(28\text{ cm}\).
| \(8 \times \square\) | \(=\) | \(32\) |
| \(32 \div 8\) | \(=\) | \(4\) |
| \(\text{width}\) | \(=\) | \(4\text{ cm}\) |
Ask: \(8\) times what makes \(32\)? The rectangle is \(4\text{ cm}\) wide. Check: \(8 \times 4 = 32\).
| \(P\) | \(=\) | \(11 \times 2 = 22\text{ m}^2\) |
| \(Q\) | \(=\) | \(7 \times 4 = 28\text{ m}^2\) |
| \(28 - 22\) | \(=\) | \(6\text{ m}^2\) |
Find both areas, then subtract. Bed Q is larger by \(6\text{ m}^2\), even though Bed P is longer.
| \(\text{area}\) | \(=\) | \(6 \times 6\) |
| \(6 \times 6\) | \(=\) | \(36\text{ cm}^2\) |
A square is a rectangle with equal sides, so multiply the side by itself. The area is \(36\text{ cm}^2\).
| \(9 \times 6\) | \(=\) | \(54\) |
| \(\text{area}\) | \(=\) | \(54\text{ m}^2\) |
Think of \(6\) rows of \(9\) square metres. The area is \(54\text{ m}^2\).
Common pitfalls
Frequently asked questions
How do you find the area of a rectangle on a grid?
Count the unit squares that cover the rectangle. The squares line up in equal rows, so you can multiply the number of rows by the number of squares in each row. For 4 rows of 7 squares the area is \(4 \times 7 = 28\text{ cm}^2\).
What is a square centimetre?
A square centimetre is a square that is 1 cm long and 1 cm wide. Its area is \(1\text{ cm}^2\). We find area by counting how many of these squares fit inside a shape.
What is the difference between area and perimeter?
Area is the number of squares that cover a shape, measured in square units. Perimeter is the distance all the way around. You add the sides for perimeter, but you multiply the rows by the columns for area.
Why do you multiply length by width to find area?
Because the unit squares sit in equal rows. Multiplying the number of rows by the number of squares in each row counts every square quickly, which is the same as length times width.
What units are used to measure area?
Area is measured in square units, such as square centimetres \((\text{cm}^2)\) or square metres \((\text{m}^2)\). Area is never written in plain centimetres.
Can two rectangles have the same area but different side lengths?
Yes. A \(3\) by \(12\) rectangle and a \(4\) by \(9\) rectangle both cover \(36\) squares, so both have an area of \(36\text{ cm}^2\) even though their side lengths are different.