Area of a rectangle

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In order to access this I need to be confident with:

Arithmetic Types of quadrilaterals

This topic is relevant for:

GCSE Maths Geometry and Measure Area

Area Of A Rectangle

Here we will learn about finding the area of a rectangle, including compound area questions, questions with missing side lengths and questions involving unit conversion.

There are also area of a rectangle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is the area of a rectangle?

The area of a rectangle is the amount of space inside the rectangle. It is measured in units squared ( $cm^{2}, m^{2}, mm^{2}$ etc.)

A rectangle is a quadrilateral ( $4$ sided shape) where every angle is a right angle ( $90°$ ) and the opposite sides are of equal length.

The area of a rectangle is calculated by multiplying the length of the rectangle by the width.

Area of a rectangle formula:

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Our final answer must be in units squared
E.g.
Square centimetres $(cm^{2})$ , square metres $(m^{2})$ , square feet $(ft^{2})$ etc.

What is the area of a rectangle?

How to find the area of a rectangle

In order to find the area of a rectangle:

Identify the length and the width
Write down the formula for the area of a rectangle
Substitute the given values and calculate
Write down your final answer with units squared

How to find the area of a rectangle

Area of a rectangle worksheet

Get your free Area of a rectangle worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Area of a rectangle worksheet

Get your free Area of a rectangle worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on area

Area of a rectangle is part of our series of lessons to support revision on area. You may find it helpful to start with the main area lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Area of a rectangle examples

Example 1: Finding area given the length and width

Find the area of the rectangle below:

Identify the length and the width

Length = $6m$

Width = $4m$

2Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

3Substitute the given values and calculate

\begin{aligned} \text { Area }_{\text {rectangle }} &=\text { length } \times \text { width } \\ \text { Area }_{\text {rectangle }} &=6 \times 4 \\ &=24 \end{aligned}

4Write down your final answer with units squared

In this case we are working with metres so our final answer must be in square metres.

$\text { Area }_{\text {rectangle }}=24 \mathrm{~m}^{2}$

Example 2: Finding the area of a rectangle requiring converting units

Find the area of the rectangle below:

Identify the length and the width

Length = $1m$

Width = $30cm$

We have two different units for the length and width so we must change the measures to a common unit.

In this case it is easier to convert both measures to centimetres to avoid working with decimals.

There are $100cm$ in $1m$ , so to convert from metres to centimetres we multiply by $100$ .

Length = $100cm$

Width = $30cm$

Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Substitute the given values and calculate

\begin{aligned} \text { Area }_{\text {rectangle }} &=\text { length } \times \text { width } \\ \text { Area }_{\text {rectangle }} &=100 \times 30 \\ &=3000 \end{aligned}

Write down your final answer with units squared

Since we are working with centimetres, our final answer will be in square centimetres.

$\text { Area }_{\text {rectangle }}=3000 \mathrm{~cm}^{2}$

Example 3: Worded question

Ms. Crawely is tiling her rectangular bathroom floor with square tiles. The dimensions of the floor are $6m$ by $4m$ , and the dimensions of each tile are $50cm$ by $50cm$ . How many tiles will she need to cover the bathroom floor?

Identify the length and the width

The bathroom floor is given in metres and the tiles are given in centimetres.
As there are two different units in the question we need to convert everything to $m$ or $cm$ . To avoid working with decimals let us convert the bathroom floor dimensions into centimetres.

For the bathroom floor:
Length = $6m\times100 = 600cm$

Width = $4m\times100 = 400cm$

For the tiles:
Length = $50cm$

Width = $50cm$

Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Substitute the given values and calculate

\begin{aligned} \text { Area }_{\text {floor }} &= \text { length } \times \text { width } \\ \text { Area }_{\text {floor }} &=600 \times 400 \\ \text { Area }_{\text {floor }} &= 240000cm^{2} \ \end{aligned}

\begin{aligned} \text { Area }_{\text {tile }} &= \text { length } \times \text { width } \\ \text { Area }_{\text {tile }} &= 50 \times 50 \\ \text { Area }_{\text {tile }} &= 2500cm^{2} \ \end{aligned}

Write down your final answer

$240000\div2500 = 96$ tiles

Example 4: Calculating side length given the area

Find the width of the rectangle below:

Identify the length and the width

Length = $80m$

Width = ?

To calculate the width of a rectangle, we need to use the area:

Area = $320m^{2}$

Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Substitute the given values and calculate

\begin{aligned} \text { Area }_{\text {rectangle }}&=\text { length } \times \text { width } \\ 320 &=80 \times w \\ \frac{320}{80}&=w \\ w&=4 \ \end{aligned}

Write down your final answer

$width=4m$

In this case, because the question asks us to calculate width and not area, the units are $m$ .

Example 5: Compound area

Find the area of the cattle field below:

Identify the length and the width

Before finding the length and width we need to first divide the compound shape into individual rectangles. In this case there are two ways in which we could do this:

Both compound shapes will give us the same answer. For the purposes of this question we will use the first compound shape.

Now we need to find the length and width of each rectangle:

We need to calculate two of the side lengths. Let us label them $a$ and $b$ . We will also label the rectangles as $A$ and $B$ .

To calculate $a$ , we know the full length of the compound shape is $8m$ . We need to subtract $7m$ from it which gives us $1m$ .

$a = 1m$

To calculate $b$ we know the full width of the compound shape is $2m$ . We need to subtract $1m$ which gives us $1m$ .

$b = 1m$

For rectangle $A$ :
Length = $2m$

Width = $1m$

For rectangle $B$ :
Length = $7m$

Width = $1m$

Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Substitute the given values and calculate

\begin{aligned} \text { Area }_{\text {rectangle A }} &= \text { length } \times \text { width } \\ \text { Area }_{\text {rectangle } A} &= 2 \times 1 \\ &= 2 \\ \\ \text { Area rectangle B } &= \text { length } \times \text { width } \\ \text { Area }_{\text {rectangle } B} &= 7 \times 1 \\ &=7\ \end{aligned}

We need to now find the sum of the area of rectangle $A$ and $B$ .

\begin{aligned} \text { Total Area } &= \text { Area }_{\text {rectangle } A}+\text { Area }_{\text {rectangle } B} \\ \text { Total Area } &=2+7 \\ \text { Total Area } &= 9 \ \end{aligned}

Write down your final answer with units squared

$Area=9m^{2}$

Example 6: Worded question

Below is a rectangle with a perimeter of $22m$ and a side length of $8m$ . Work out the area of the rectangle.

Identify the length and the width

Length = $8m$

Width = ?

As the width is unknown we will have to calculate it using the perimeter.

The formula for the perimeter of a rectangle is:

$P=2 l+2 w$

We now need to substitute the values that we know.

\begin{aligned} &P=2 l+2 w \\ &22=2(8)+2 w \\ &22=16+2 w \\ \end{aligned}

Now isolate the $w$ by moving all the terms to the other side of the equal

\begin{aligned} &2 w=6 \\ &w=3 \end{aligned}

Length = $8m$

Width = $3m$

Write down the formula for the area of a rectangle

$\text { Area }_{\text {rectangle }}=\text { length } \times \text { width }$

Substitute the given values and calculate

\[\begin{aligned} \text { Area }_{\text {rectangle }} &=\text { length } \times \text { width } \\ \text { Area }_{\text {rectangle }} &=8 \times 3 \\ &=24 \end{aligned}\]

Write down your final answer with units squared

In this case we are working with metres so our final answer must be in square metres.

$\text { Area }_{\text {rectangle }} =24m^{2}$

Common misconceptions

Using incorrect units for the answer

A common error is to forget to include squared units when asked to calculate area.

Forgetting to convert measures to a common unit

Before using the formula for calculating the area of a rectangle we need to ensure that units are the same. If different units are given (E.g. length = $4m$ and width = $3cm$ ) then you must convert them either both to $cm$ or both to $m$ .

Practice area of a rectangle questions

60mm

60mm^{2}

17mm^{2}

17mm

Multiply the length and width together to get the area of the rectangle.

480m^{2}

480cm^{2}

$4.8m^{2}$ or $48000cm^{2}$

124m^{2}

Prior to multiplying the length times the width, convert the length and width to a common unit (both length and width to $m$ or both to $cm$ ). Remember there are $100cm$ in $1m$ .

$875$ tiles

$35$ tiles

$400$ tiles

$11$ tiles

Convert the length and width to a common unit remembering that there are $100cm$ in $1m$ . Find the area of the floor by multiplying the length of the rectangle by the width. Divide the area of the floor by the area of the tile to get the number of tiles needed to cover the floor.

19600m

19600m^{2}

4m^{2}

4m

Using the formula for the area of a rectangle we substitute our given values. As we are trying to calculate the width of the rectangle we need to rearrange the formula to divide the length into the area.

22m^{2}

57m^{2}

30m^{2}

45m^{2}

Split the compound shape into $3$ rectangles. Calculate the missing side length of rectangle $C$ by subtracting $3$ from the total length which is $5m$ . Work out the area of $A$ , $B$ and $C$ and then add up all the individual areas to get the total area of the compound shape.

\begin{aligned} \text { Area }_{\text {rectangle } A} &=\text { length } \times \text { width } \\ &=3 \times 2 \\ &=6m^{2} \\ \\ \text { Area }_{\text {rectangle } B} &=\text { length } \times \text { width } \\ &=3 \times 2 \\ &=6m^{2} \\ \\ \text { Area }_{\text {rectangle } C} &=\text { length } \times \text { width } \\ &=9 \times 2 \\ &=18m^{2} \\ \\ \text { Total Area } &=6 m^{2}+6 m^{2}+18 m^{2} \\ &=30 \mathrm{~m}^{2} \end{aligned}

22m^{2}

2m

2m^{2}

22m

Using the formula for the perimeter of a rectangle, substitute the perimeter and the length to solve for width. Then use the area of a rectangle formula to calculate the area.

Area of a rectangle GCSE questions

1. Shown below is a rectangle. Work out the area of the rectangle.

(2 marks)

Show answer

12\times4

(1)

48m^{2}

(1)

2. A gardener is planning a new rectangular garden. It will feature two identical square flower beds and the rest will be covered with grass. Calculate the area that will be covered by grass.

(4 marks)

Show answer

$15\times7$ and $4\times4$

(1)

$105$ or $16$ or $32$ seen

(1)

105 - 16 - 16

(1)

73m^{2}

(1)

3. Sarah wants to tile her bathroom floor. The dimensions of the bathroom are $6m$ by $3m$ . She plans to buy square $50cm$ tiles costing $£2.50$ each. How much will it cost to tile her entire bathroom floor?

(5 marks)

Show answer

Converting all dimensions to either metres or centimetres
$6m = 600cm, 3m = 300cm$ or $50cm = 0.5m$

(1)

$6 \times 3$ and $50cm \times 50cm$

(1)

Dividing the area of the bathroom floor by the area of the tile
$18\div 0.25 =72$ tiles or $180000\div 2500 =72$ tiles

(1)

72 \times £2.50

(1)

£180

(1)

Learning checklist

You have now learned how to:

Calculate and compare the area of rectangles using standard units

Calculate the area of rectangles and related composite shapes

The next lessons are

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Introduction

What is the area of a rectangle?

How to find the area of a rectangle

Area of a rectangle worksheet

Area of a rectangle examples

↓

Example 1: finding area given the length and width Example 2: finding the area of a rectangle requiring converting units Example 3: worded question Example 4: calculating side length given the area Example 5: compound area Example 6: worded question

Common misconceptions

Practice area of a rectangle questions

Area of a rectangle GCSE questions

Learning checklist

Next lessons

Still stuck?