Area of a rectangle

Q: What is the formula for the area of a rectangle?

Area = length × width, written A = l \times w.

Q: What units is area measured in?

Square units: mm², cm², m², km², or square inches and feet. Always write the square.

The area of a rectangle is the amount of flat space inside it. You find it by multiplying its length by its width, and the answer is always in square units such as $cm^{2}, m^{2}$ or square feet.

Formulas

Area of a rectangle

A = l \times w

Missing width (when the area and length are known)

w = \frac{A}{l}

Area of a square (a rectangle with equal sides)

A = s \times s = s^{2}

Worked examples

Example 1. A rectangular garden is 12 m long and 7 m wide. What is its area?

Area = length × width.
$A = 12 \times 7 = 84$ .

Answer:

84 m^{2}

Example 2. A rectangle has an area of

150 cm^{2}

and a length of 25 cm. Find its width.

Width = area ÷ length.
$w = 150 \div 25 = 6$ .

Answer: 6 cm

Example 3. A rectangle is 2 m long and 50 cm wide. Find its area in

cm^{2}

The units must match, so change 2 m to 200 cm.
$A = 200 \times 50 = 10000$ .

Answer:

10000 cm^{2}

Example 4. A floor measures 5 m by 4 m. It is covered with square tiles of side 50 cm. How many tiles are needed?

Floor area = $5 \times 4 = 20 m^{2}$ .
One tile = $0.5 \times 0.5 = 0.25 m^{2}$ .
Tiles = $20 \div 0.25 = 80$ .

Answer: 80 tiles

Common mistakes

Mixing units, for example metres with centimetres. Convert both sides to the same unit first.
Adding the sides instead of multiplying. Adding (and doubling) gives the perimeter, not the area.
Writing cm instead of $cm^{2}$ . Area is measured in square units.

Practice questions with answers

1. The formula for the area of a rectangle is:

Alength $x$ breadth
Blength + breadth
C $2 \times$ (length + breadth)
Dside $x$ side

Show answer

Answer: A) length

x

breadth

Area of a rectangle = length

x

breadth.

2. A floor is 8 m long and 6 m wide. Square tiles of side 2 m are used to cover it. How many tiles are needed?

Show answer

Answer: D) 12

Floor area =

8 \times 6 = 48 m^{2}

. Each tile area =

2 \times 2 = 4 m^{2}

. Number of tiles = 48 ÷ 4 = 12.

3. A rectangular hall floor is 30 m by 24 m.
It is divided into identical square sections, each of the largest possible equal size that fits exactly along both sides.
What is the area of one such square section?

A36 sq m
B24 sq m
C144 sq m
D12 sq m

Show answer

Answer: A) 36 sq m

The largest square that fits exactly along 30 and 24 has side = HCF(30, 24) = 6 m. Section area =

6 \times 6 = 36

sq m.

4. A room floor measures 6 m by 4.5 m. Square tiles of side 30 cm are used to cover it completely. How many tiles are needed?

A300
B30
C90
D3000

Show answer

Answer: A) 300

Floor =

6 \times 4.5 = 27 m^{2}

. A tile of side 30 cm = 0.3 m covers

0.3 \times 0.3 = 0.09 m^{2}

. Tiles = 27 ÷ 0.09 = 300. Converting only once and taking the tile as

0.9 m^{2}

gives the trap 30; dividing by the side 0.3 m gives 90.

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Frequently asked questions

What is the formula for the area of a rectangle?

Area = length × width, written $A = l \times w$ .

How is the area of a rectangle different from its perimeter?

Area measures the space inside (square units). Perimeter measures the distance around the edge (ordinary units). A rectangle 8 cm by 3 cm has area $24 cm^{2}$ and perimeter 22 cm.

How do you find the area if you only know the perimeter and one side?

Half the perimeter equals length + width, so subtract the known side to get the other. For a perimeter of 30 cm and a length of 9 cm: width = 15 − 9 = 6 cm, so the area is $9 \times 6 = 54 cm^{2}$ .

What units is area measured in?

Square units: $mm^{2}, cm^{2}, m^{2}, km^{2}$ , or square inches and feet. Always write the square.

Area of a rectangle

Formulas

Worked examples

Common mistakes

Practice questions with answers

Practice by class

Frequently asked questions

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