GCSE Maths Geometry and Measure Area

Area Of A Rectangle

# 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.

## How to find the area of a rectangle

In order to find the area of a rectangle:

1. Identify the length and the width
2. Write down the formula for the area of a rectangle
3. Substitute the given values and calculate

## 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:

1. 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}

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

Write down the formula for the area of a rectangle

Substitute the given values and calculate

### 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

Write down the formula for the area of a rectangle

Substitute the given values and calculate

### Example 4: Calculating side length given the area

Find the width of the rectangle below:

Identify the length and the width

Write down the formula for the area of a rectangle

Substitute the given values and calculate

### Example 5: Compound area

Find the area of the cattle field below:

Identify the length and the width

Write down the formula for the area of a rectangle

Substitute the given values and calculate

### 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

Write down the formula for the area of a rectangle

Substitute the given values and calculate

### 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

1. Find the area of the rectangle below:

60mm

60mm^{2}

17mm^{2}

17mm

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

2. Find the area of the rectangle below:

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 .

3. Mr. Measure is tiling his rectangular kitchen floor with square tiles. The dimensions of the floor are 7m by 5m and the dimensions of each tile are 20cm by 20cm . How many tiles will he need to cover the bathroom floor?

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.

4. Find the width of the rectangle below:

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.

5. Below is a plan for a new flower bed. Find the area of the flower bed.

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}

6. Below is a rectangle with a perimeter of 26m and a side length of 11m . Work out the area of the rectangle.

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)

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)

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)

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

## Still stuck?

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