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GCSE Maths Geometry and Measure Area

Area Of A Parallelogram

Area Of A Parallelogram

Here we will learn how to find the area of a parallelogram, including compound area questions, questions with missing side lengths and questions involving unit conversion.

There are also area of a area of a parallelogram 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 parallelogram?

The area of a parallelogram is the amount of space inside a parallelogram. It is measured in units squared (cm2,m2,mm2 cm^{2}, m^{2}, mm^{2} etc.)

A parallelogram is a quadrilateral (4 4 sided shape) with 2 2 pairs of parallel sides. The parallel sides are the same length and the opposite angles are equal. The interior angles of the parallelogram add up to 360Β° 360Β° .

area of a parallelogram image 1

The area of a parallelogram is calculated by multiplying the base of a parallelogram by its perpendicular height.

Area of a parallelogram formula:

\[\begin{aligned} \text { Area }_{\text {parallelogram }}&=\text { base } \times \text { perpendicular height } \\ \text { Area }_{\text {parallelogram }}&=b \times h \end{aligned}\]

area of a parallelogram image 2

Let’s see why this works:

area of a parallelogram image 3

If we cut off the triangle at one end of a parallelogram and attach it to the other we form a rectangle. The formula for the area of a rectangle is lengthΓ—width length\times width (or in this case baseΓ—height base \times height).

Our final answer must be in units squared
E.g. square centimetres (cm2) cm^{2}) , square metres (m2 m^{2} ), square feet (ft2 ft^{2} ) etc.

What is the area of a parallelogram?

What is the area of a parallelogram?

Parallelogram


A parallelogram is a 2D shape with opposite sides that are both parallel and equal in length. The diagonals of a parallelogram bisect each other. We can categorise them as quadrilaterals because they have 4 sides.

parallelogram paragraph image 1 300x256

We need to be able to identify the three special types of parallelograms.  

E.g.

A parallelogram where all sides are equal is a rhombus.

parallelogram paragraph image 2 300x174

E.g.

A parallelogram in which all angles are right angles, and the diagonals are equal is a rectangle.

parallelogram paragraph image 3 300x241

E.g.

A parallelogram with all equal sides and all angles equal to 90 degree, and equal diagonals is a square.

parallelogram paragraph image 4 257x300

A parallelogram is, essentially, a slanted rectangle, so we can use the same calculation to find the area of a parallelogram as you would calculate the area of a rectangle, as long as you use the perpendicular height rather than the slant length. 

E.g.

Calculate the area of the parallelogram.

parallelogram paragraph image 5 300x155

Area = 10 x 6 = 60 

Let’s explore more about parallelograms below.

How to find the area of a parallelogram

In order to find the area of a parallelogram:

  1. Identify the base and the perpendicular height of the parallelogram.
  2. Write down the formula for the area of a parallelogram.
  3. Substitute the given values and calculate.
  4. Write down your final answer with units squared.

How to find the area of a parallelogram

How to find the area of a parallelogram

Area of a parallelogram worksheet

Area of a parallelogram worksheet

Area of a parallelogram worksheet

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

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Area of a parallelogram worksheet

Area of a parallelogram worksheet

Area of a parallelogram worksheet

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

DOWNLOAD FREE

Related lessons on area

Area of a parallelogram 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 parallelogram examples

Example 1: finding area given the base and perpendicular height

Find the area of the parallelogram below:

area of a parallelogram example 1

  1. Identify the base and perpendicular height of the parallelogram.

Base = 10m 10m

Perpendicular height = 6m 6m

2Write down the formula for the area of a parallelogram.

 Area  parallelogram = Base Γ— Perpendicular Height  \text { Area }_{ \text { parallelogram }}=\text { Base } \times \text { Perpendicular Height }

3Substitute the given values and calculate.

\[\begin{aligned} \text { Area }_{\text {parallelogram }}&=\text { Base } \times \text { Perpendicular Height } \\ &=10 \times 6 \\ &=60 \end{aligned}\]

4Write down your final answer with units squared.

 Area parallelogram =60 m2 \text { Area }_{\text {parallelogram }}=60 \mathrm{~m}^{2}

Example 2: finding the area of a parallelogram requiring converting units

Find the area of the parallelogram below:

area of a parallelogram example 2

Identify the base and perpendicular height of the parallelogram.

Show step

Write down the formula for the area of a parallelogram.

Show step

Substitute the given values and calculate.

Show step

Write down your final answer with units squared.

Show step

Example 3: worded question

A painter is painting a logo on the side of an office block. The logo is composed of four identical parallelograms and is shown below. Each tin of paint costs Β£1.20 Β£1.20 and contains enough paint to cover an area of 2.5m2 2.5m^{2} . How much will it cost to paint the logo?

area of a parallelogram example 3

Identify the base and perpendicular height of the parallelogram.

Show step

Write down the formula for the area of a parallelogram.

Show step

Substitute the given values and calculate.

Show step

Write down your final answer.

Show step

Example 4: calculating base length given the area

Find the base length of the parallelogram below:

area of a parallelogram example 4

Identify the base and perpendicular height of the parallelogram.

Show step

Write down the formula for the area of a parallelogram.

Show step

Substitute the given values and calculate.

Show step

Write down your final answer.

Show step

Example 5: compound area

Calculate the area of the shaded region below:

area of a parallelogram example 5

Identify the base and perpendicular height of the parallelogram.

Show step

Write down the formula for the area of a parallelogram.

Show step

Substitute the given values and calculate.

Show step

Write down your final answer with units squared.

Show step

Example 6: finding the area involving algebra question

Calculate the value of x x in the parallelogram below:

area of a parallelogram example 6

Identify the base and perpendicular height of the parallelogram.

Show step

Write down the formula for the area of a parallelogram.

Show step

Substitute the given values and calculate.

Show step

Write down your final answer.

Show step

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 parallelogram, we need to ensure the units used are the same. If different units are given (E.g. length = 4m 4m and width = 3cm 3cm ) we must convert them both to either cm cm or both to m m .

  • Length of the slanted side and perpendicular height

Sometimes in a question we are given additional lengths which are not needed in our calculations. An example of this is being given the length of one of the slanted sides of the parallelogram. To calculate the area we must ignore the slant length and instead use the vertical height.

Practice Area of a parallelogram questions

1. Find the area of the parallelogram below:

 

area of a parallelogram practice question 1

17.5m 17.5m
GCSE Quiz False

66m2 66m^{2}
GCSE Quiz True

17.5m 17.5m
GCSE Quiz False

66m 66m
GCSE Quiz False

bΓ— h=12Γ—5.5=66m2 b \times  h = 12 \times 5.5 = 66m^{2}. Remember to have units squared in your final answer.

2. Find the area of the parallelogram below:

 

area of a parallelogram practice question 2

31.5m2 31.5m^{2}
GCSE Quiz True

3150m2 3150m^{2}
GCSE Quiz False

22.4m2 22.4m^{2}
GCSE Quiz False

14.4m2 14.4m^{2}
GCSE Quiz False

Convert 450cm 450cm into metres by dividing by 100 100 . Multiply the base length (7m) (7m) by the converted perpendicular height (4.5m) (4.5m) to equal 31.5m2 31.5m^{2} . Be careful not to multiply by the length of the diagonal instead of the perpendicular height.

3. Calculate the area of the garden below:

 

area of a parallelogram practice question 3

25.2m2 25.2m^{2}
GCSE Quiz False

12.2m2 12.2m^{2}
GCSE Quiz False

31.2m2 31.2m^{2}
GCSE Quiz True

37.2m2 37.2m^{2}
GCSE Quiz False

Find the area of the parallelogram by multiplying the base length and the height. Find the area of the triangle by multiplying the base and the height and dividing by 2 2 . Add together the area of the triangle and parallelogram.

4. Calculate the length of the base of the parallelogram below:

 

area of a parallelogram practice question 4

22cm 22cm
GCSE Quiz True

2662cm2 2662cm^{2}
GCSE Quiz False

22cm2 22cm^{2}
GCSE Quiz False

2662cm 2662cm
GCSE Quiz False

Divide the area by the perpendicular height of 11m 11m . Remember that you are not calculating the area so your final answer should not be in units squared.

5. Calculate the area of the shaded region below:

 

area of a parallelogram practice question 5

126cm2 126cm^{2}
GCSE Quiz False

224cm2 224cm^{2}
GCSE Quiz True

98cm2 98cm^{2}
GCSE Quiz False

126.98cm2 126.98cm^{2}
GCSE Quiz False

Convert all measures to cm cm . Find the area of the parallelogram first by multiplying the base times the height. Add on the area of the rectangle which is calculated by multiplying the length and the width.

6. Calculate the base length in the parallelogram below:

 

area of a parallelogram practice question 6

4cm 4cm
GCSE Quiz False

5cm 5cm
GCSE Quiz True

16cm 16cm
GCSE Quiz False

33cm 33cm
GCSE Quiz False

Multiply the base times the perpendicular height, Remember to multiply the two by both terms. Rearrange the equation to calculate x x . Substitute the value of x x back into 4xβˆ’11 4x-11 to calculate the base length.

Area of a parallelogram GCSE questions

1. Find the area of the parallelogram. Remember to show your full working.

 

area of a parallelogram gcse question 1

 

(2 marks)

Show answer
38Γ—19 38\times19

(1)

722m2 722m^{2}

(1)

2.  A landscaper is planning a rectangular garden for a client. The garden will feature a patio and sandpit both in the shape of parallelograms. The remainder of the garden will be covered in grass. Below is a blueprint of the garden.
(a)What area of the garden will be covered in grass?

 

area of a parallelogram gcse question 2a

 

(b) A roll of grass covers an area of 3m2 3m^{2} and costs Β£14.50 Β£14.50 . How much will it cost to put grass in the garden?

 

(7 marks)

Show answer

(a)
Area of rectangle = 15Γ—7=105 15\times7 = 105

(1)

Area of both parallelograms: 5Γ—4=20 5\times4 = 20 and 4.5Γ—1.5=6.75 4.5\times1.5 = 6.75

(1)

Area of rectangle – area of parallelograms=  105–20–6.75 105 – 20 – 6.75

(1)

78.25m2 78.25m^{2}

(1)

(b)
78.25Γ·3=26.08 78.25\div3 = 26.08 rolls of grass

(1)

27Γ—14.5 27\times14.5

(1)

Β£391.50 Β£391.50

(1)

3. Calculate the value of x x in the diagram below:

 

area of a parallelogram gcse question 3

 

(4 marks)

Show answer
6Γ—(3xβˆ’9) 6 \times (3x-9)

(1)

18xβˆ’54=36 18x-54=36

(1)

Evidence of rearranging equation to solve for x x

(1)

x=5 x = 5

(1)

Learning checklist

You have now learned how to:

  • Calculate and compare the area of parallelograms using standard units
  • Calculate the area of parallelograms and related composite shapes

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