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Area of a Parallelogram

In this worksheet students will learn the formula for finding the area of a parallelogram and be able to find areas and solve simple problems.

'Area of a Parallelogram' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Area Calculations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Parallelogram.  Another 2-dimensional shape that we easily recognise, but can't always remember its name.

 

It has opposite parallel sides, which may help with remembering the name.

 

 

What examples can you think of that we see in everyday life?

 

 

Probably not so obvious to think about.  

 

Believe it or not, you can be two things at once!

 

For example, a square has two sets of parallel sides, so is also a parallelogram but we call it a square. The same goes for a rectangle.

Basically a parallelogram is a four-sided shape with their opposite sides equal in length (the same as a square or rectangle).

 

 

Mathematicians can be awkward and make a four-sided look different just for fun, so that's how we arrive at parallelogram.

 

There are all sorts of reasons we may need to know the area of a parallelogram

 

Before we can do any of this there is one thing we need to know and that is how to find the area of a parallelogram.

 

First of all, we know that the sides of a parallelogram are not all the same length. 

 

Two sides will have one length and the other two sides a different length.

 

As with a lot of shape work, there is a formula that you need to learn. So here goes:

 

Area of a parallelogram =base x height

 

You may recognise that it is the same as the formula for the area of a square and a rectangle.

Find the area of the parallelogram below.

 

 

Area = base x height

Hang on!! We cannot work out the area of the parallelogram above as we only know the slanted height!

 

Let's try this one instead.

 

 

 Look out!  You need to work with the vertical height, not the slanted height.

12 x 5 = 60 cm²

 

As we are working with area units are always squared. e.g cm² m²

 

What a bargain - one formula for three shapes.

 

 

Find the area of this parallelogram. 

14 cm²

36 cm²

60 cm²

64 cm²

Match the area to the correct parallelogram.

Column A

Column B

Parallelogram sides 4 cm and height of 3 cm
62.05 cm²
Parallelogram sides 6 cm and height of 5 cm
33 cm²
Parallelogram sides 11 cm and height of 3 cm
22.26 m²
Parallelogram sides 8.5 cm and height of 7.3 cm
20 mm²
Parallelogram sides 4 cm and and height of 5 cm
12 cm²
Parallelogram sides 5.3 m x and height of 4.2 m
30 cm²

 

Find the area of this parallelogram.  

Column A

Column B

Parallelogram sides 4 cm and height of 3 cm
62.05 cm²
Parallelogram sides 6 cm and height of 5 cm
33 cm²
Parallelogram sides 11 cm and height of 3 cm
22.26 m²
Parallelogram sides 8.5 cm and height of 7.3 cm
20 mm²
Parallelogram sides 4 cm and and height of 5 cm
12 cm²
Parallelogram sides 5.3 m x and height of 4.2 m
30 cm²

 

A farmer has a  parallelogram pen for his horses measuring  2.7m along one fence line and 212 cm along the other fence line. 

What is the area of the floor of the barn?  There are two possible answers.

57240 cm²

5.624 m²

5.724 m²

5.64 m²

 

What is the difference in area between a parallelogram with side lengths of 28 cm and a height of 4 cm and a parallelogram with side lengths of 37 cm and a height of 5.5 cm?

Round your answer to 1 decimal place

57240 cm²

5.624 m²

5.724 m²

5.64 m²

 

Two new rugs in the shape of a parallelogram have been bought for this families living room.

One rug measures  4 m long with a height of 2 m.  The other is 6 m in length and has a height of 4m.  What is the total area of the rugs?

32 cm²

24 m²

32 m²

16 m²

 

What is the area of these parallelograms?

 80 cm²18 cm²84 cm²19 cm²Unsure as we do not know the vertical height
Parallelogram A
Parallelogram B

 

This mosaic is going to have parallelogram tiles placed around it.  The tiles are painted, Brown, beige and black.

 

The brown parallelograms have sides of  3 cm and a vertical height of 2 cm

The beige parallelograms have sides of  3 cm and a vertical height of 2.5 cm

The black parallelograms have sides of 3 cm and a vertical height of 1.5 cm

 

4 brown, 3 beige and 2 black tiles are used.  What is the total area of tiles used?

 

State your answer to 1 decimal place.

 80 cm²18 cm²84 cm²19 cm²Unsure as we do not know the vertical height
Parallelogram A
Parallelogram B

 

What is the  area of this rectangle with sides 2x and  a height of x - 6

There are two correct answers.

3x - 6

2x multiplied by x - 6

x - 6

2x² - 12x

What is the area of a parallelogram with sides 6 cm and a height of 3x + 6

There are two correct answers.

15x

6x multiplied by 3x + 6

9x multiplied by 36x

9x multiplied by 36

  • Question 1

 

Find the area of this parallelogram. 

CORRECT ANSWER
60 cm²
EDDIE SAYS
Did you apply the formula? Base x Height When working with the area of a parallelogram you are usually given both side lengths. Sometimes however there are sometimes three numbers given. Remember you need the vertical height. 12 x 5 = 60 cm²
  • Question 2

Match the area to the correct parallelogram.

CORRECT ANSWER

Column A

Column B

Parallelogram sides 4 cm and heig...
12 cm²
Parallelogram sides 6 cm and heig...
30 cm²
Parallelogram sides 11 cm and hei...
33 cm²
Parallelogram sides 8.5 cm and he...
62.05 cm²
Parallelogram sides 4 cm and and ...
20 mm²
Parallelogram sides 5.3 m x and h...
22.26 m²
EDDIE SAYS
Applying the formula is now getting easy. Make sure you read both numbers carefully 4 x 3 = 12 cm² 5 x 6 = 30 cm² 11 x 3 = 33 cm² 8 .5 x 7.3 = 62.05 cm² 4 x 5 = 20 cm² 5.2 x 4.2 = 22.26 cm² You're usually asked to round to 1 or 2 decimal places.
  • Question 3

 

Find the area of this parallelogram.  

CORRECT ANSWER
EDDIE SAYS
There's nothing to it, is there? 2 x 7 = 14 cm² Providing you select the correct numbers you will never go wrong.
  • Question 4

 

A farmer has a  parallelogram pen for his horses measuring  2.7m along one fence line and 212 cm along the other fence line. 

What is the area of the floor of the barn?  There are two possible answers.

CORRECT ANSWER
57240 cm²
5.724 m²
EDDIE SAYS
Often area questions will give two different units of measurement. You will need your eagle eye for this. You can convert either way. 2.7 m = 270 cm 270 x 212 =57,240 cm² or 212 cm = 2.12 m 2.7 x 2.12 =5.724 (5.73 to 3 d.p) Nay bother for you.
  • Question 5

 

What is the difference in area between a parallelogram with side lengths of 28 cm and a height of 4 cm and a parallelogram with side lengths of 37 cm and a height of 5.5 cm?

Round your answer to 1 decimal place

CORRECT ANSWER
EDDIE SAYS
Just another example of finding area from a written question. 28 x 4 = 112 cm² 37 x 5.5 = 203.5 cm² 203.5 - 112 = 91.5 cm² The word difference in a question should lead you to subtract.
  • Question 6

 

Two new rugs in the shape of a parallelogram have been bought for this families living room.

One rug measures  4 m long with a height of 2 m.  The other is 6 m in length and has a height of 4m.  What is the total area of the rugs?

CORRECT ANSWER
32 m²
EDDIE SAYS
This is just a simple 2 step question. You have all the knowledge that you need. Area of rug 1 = 4 x 2 = 8 m² Area of rug 2 = 6 x 4 = 24 m² Add the two together 8 + 24 = 32 m²
  • Question 7

 

What is the area of these parallelograms?

CORRECT ANSWER
 80 cm²18 cm²84 cm²19 cm²Unsure as we do not know the vertical height
Parallelogram A
Parallelogram B
EDDIE SAYS
Did you remember the vertical height is required? Without if we can't find the area? We can only find the area of rectangle A. 10 x 8 = 80 cm²
  • Question 8

 

This mosaic is going to have parallelogram tiles placed around it.  The tiles are painted, Brown, beige and black.

 

The brown parallelograms have sides of  3 cm and a vertical height of 2 cm

The beige parallelograms have sides of  3 cm and a vertical height of 2.5 cm

The black parallelograms have sides of 3 cm and a vertical height of 1.5 cm

 

4 brown, 3 beige and 2 black tiles are used.  What is the total area of tiles used?

 

State your answer to 1 decimal place.

CORRECT ANSWER
EDDIE SAYS
Find the area of each coloured parallelogram. Multiply it up by the number required for the mosaic. Add them all together. Brown 3 x 2 = 6 x 4 = 24 Beige 3 x 2.5 = 7.5 x 3 = 22.5 Black 3 x 1.5 =4.5 x 2 = 9 24 + 22.5 + 9 = 55.5 cm²
  • Question 9

 

What is the  area of this rectangle with sides 2x and  a height of x - 6

There are two correct answers.

CORRECT ANSWER
2x multiplied by x - 6
2x² - 12x
EDDIE SAYS
I know what you are thinking... eeekkk! This is easier than it looks. We know that 1 side is length 2x The height is x -6 We don't know what x is so all we can write is: 2x multiplied by x - 6 or if you want to show off 2x times x = 2x² 2x times -6 = -12x which is 2x² -12x
  • Question 10

What is the area of a parallelogram with sides 6 cm and a height of 3x + 6

There are two correct answers.

CORRECT ANSWER
6x multiplied by 3x + 6
9x multiplied by 36
EDDIE SAYS
Bring it on!! 6 multiplied by 3x + 6. (one side multiplied by the other) or showing off again 9x + 36 If you don't know how I got 9x + 36. Look at multiplying out brackets.
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