# Understanding Rectangles

In this worksheet, students will be asked to find missing lengths of rectangles from their given area. Students will also be asked to calculate perimeter once a missing length has been found.

Key stage:  KS 2

Curriculum topic:   Geometry: Properties of Shapes

Curriculum subtopic:   Understand Rectangles

Difficulty level:

### QUESTION 1 of 10

A rectangle is a 4-sided flat shape made of straight sides, where all four of its interior angles are 90°.

In this activity, you will be asked to find the area and perimeter of rectangles.

You will also have to find the missing lengths of rectangles.

Key formula to remember:

Area of a rectangle = length x width

Perimeter = length + width + length + width

Want to understand this further and learn how this links to other topics in maths?

Why not watch this video?

This rectangle has an area of 12 cm² and a width of 3 cm.

What is the length of the rectangle?

4.5 cm

5 cm

4 cm

6 cm

Look at the rectangle below.

It has an area of 96 cm². It has a width of 8 cm.

What must its length be?

Complete the blank space.

4.5 cm

5 cm

4 cm

6 cm

Look at the rectangle below.

The length is 14 cm and the area is 126 cm² .

What is the width?

4.5 cm

5 cm

4 cm

6 cm

Look at the rectangle below.

The length is 16 cm and the area is 224 cm².

What is the width?

4.5 cm

5 cm

4 cm

6 cm

The rectangle below has an area of 84 cm².

Can you choose the correct width and length?

 13cm and 7cm 7cm and 12cm 14cm and 7cm 9cm and 12cm Width and Length of Rectangle

The rectangle below has an area of 336 cm².

 40 cm and 7 cm 34 cm and 6 cm 42 cm and 8 cm 43 cm and 8 cm Width and Length of Rectangle

The rectangle below has an area of 336 cm².

In the previous question, you calculated the width as 8 cm and the length as 42 cm.

What is the perimeter of the rectangle?

 40 cm and 7 cm 34 cm and 6 cm 42 cm and 8 cm 43 cm and 8 cm Width and Length of Rectangle

Can you work out the length of side a?

When you have done this, can you choose the correct perimeter for the shape below?

40 cm

54 cm

52 cm

45 cm

Can you work out the length of side a?

When you have done this, write the perimeter for the shape below in cm.

Can you work out the length of side a?

When you have done this, can you write the perimeter for the shape below in cm?

• Question 1

This rectangle has an area of 12 cm² and a width of 3 cm.

What is the length of the rectangle?

4 cm
EDDIE SAYS
To find the area of a rectangle, we have to multiply the length by width. If we know the area of the rectangle is 12 cm² and the width is 3 cm, we can then divide 12 by 3 to get the answer of 4 cm. We can check this by doing the following calculation 4 x 3 = 12 cm²
• Question 2

Look at the rectangle below.

It has an area of 96 cm². It has a width of 8 cm.

What must its length be?

Complete the blank space.

EDDIE SAYS
Again, we must recall the formula, area = length x width. If we know the area is 96 cm² and the width is 8 cm, we have to divide 96 by 8 = 12. We can check this with the calculation 8 x 12 = 96 cm². Hopefully, this is beginning to get easier for you. Let's continue...
• Question 3

Look at the rectangle below.

The length is 14 cm and the area is 126 cm² .

What is the width?

EDDIE SAYS
If we divide the area of 126 cm² by the given length of 14, we get the answer 9. We can check this using the formula for finding the area 14 x 9 = 126 cm².
• Question 4

Look at the rectangle below.

The length is 16 cm and the area is 224 cm².

What is the width?

EDDIE SAYS
If we divide the area of 224 cm² by the given length of 16, we are given the answer of 14. We can check this using the formula for finding the area 16 x 14 = 224 cm²
• Question 5

The rectangle below has an area of 84 cm².

Can you choose the correct width and length?

 13cm and 7cm 7cm and 12cm 14cm and 7cm 9cm and 12cm Width and Length of Rectangle
EDDIE SAYS
How did you get on? The correct width and length of the rectangle are 7cm and 12cm. Area = 7 x 12 = 84 cm² . You're getting good at this! You're now halfway.
• Question 6

The rectangle below has an area of 336 cm².

 40 cm and 7 cm 34 cm and 6 cm 42 cm and 8 cm 43 cm and 8 cm Width and Length of Rectangle
EDDIE SAYS
The correct width and length of the rectangle are 8 cm and 42 cm. Area = 8 x 42 = 336 cm² .
• Question 7

The rectangle below has an area of 336 cm².

In the previous question, you calculated the width as 8 cm and the length as 42 cm.

What is the perimeter of the rectangle?

EDDIE SAYS
To find the perimeter we calculate length + width + length + width. 42 + 42 + 8 + 8= 100 cm Another way we can calculate the perimeter is by doubling the length, doubling the width and adding both together. 42 x 2 = 84 8 x 2 = 16 84 + 16 = 100 cm Simple, right?
• Question 8

Can you work out the length of side a?

When you have done this, can you choose the correct perimeter for the shape below?

52 cm
EDDIE SAYS
First, to find side a, we need to do the calculation 18 - 5 = 13 Side a = 13cm Then, add together each of the sides 12 + 18 + 6 + 5 + 13 = 54 cm
• Question 9

Can you work out the length of side a?

When you have done this, write the perimeter for the shape below in cm.

30cm
30 cm
30 centimetres
30centimetres
EDDIE SAYS
First, in order to find side a, we need to do the calculation 9 - 3 = 6 Side a = 6 cm Then, add together each of the sides 8 + 3 + 4 + 9 + 6 = 30 cm Great focus, you're almost complete! Then you can take a well-deserved break.
• Question 10

Can you work out the length of side a?

When you have done this, can you write the perimeter for the shape below in cm?

56 cm
56cm
56 centimetres
56
EDDIE SAYS
Firstly, in order to find side a, we need to do the calculation 18 - 5 = 13 Side a = 13 cm Then, we need to add together each of the sides. 13 + 14 + 5 + 18 + 6 = 56 cm Great work! We hope you’ve improved your knowledge of rectangles.
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