# Finding Length of Unknown Sides

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## Finding the Length of Unknown Sides

To find the length of missing sides on a rectangle;

• Add together known side lengths
• Subtract total from perimeter
• If the shape is a rectangle with unknown opposite sides, divide the answer by two
• If it is a shape with 1 unknown side, the answer is the length

Below you will find a worksheet on finding the length of unknown sides.

## Finding Length of Unknown Sides exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Finding Length of Unknown Sides.
• ### How can we find the missing lengths of the sides?

Hints

Look at the perimeter. Remember, this is the total length of all sides added together.

What shape is this piece of climbing wall? What does that tell us?

What should we do at the end to make sure we have the correct answer?

Solution
1. First, add together the known side lengths. 8 + 8 = 16.
2. Then, subtract the total of the known side lengths from the perimeter. 24 - 16 = 8.
3. This shape is a rectangle so opposite sides are equal. We therefore divide 8 by 2 to get 4.
4. Check your work by adding all of the sides together. 8 + 8 + 4 + 4 = 24.
• ### What are the missing lengths of the sides on this piece?

Hints

What is the total of the known side lengths? Work this out and then subtract it from the perimeter.

After subtracting, divide what is left by two as this shape is a rectangle.

Solution

The missing side lengths are 7 units each.

• 2 + 2 = 4.
• If we subtract 4 from 18, we get 14.
• We then divide 14 by 2, to get 7.
• Therefore the missing side lengths are 7 units each.
• ### What are the missing side lengths of these pieces?

Hints

Add up the given side lengths first.

If the shape is only missing one side length, subtract the total of the given lengths from the perimeter. This is your answer.

If your shape is a rectangle:

• Subtract the total of the given lengths from the perimeter.
• Divide this by two.

Solution
• The first shape had two missing side lengths of 6 units each.
• The second shape had two missing side lengths of 2 units each.
• The third shape had a missing side length of 3 units.
• The fourth shape had a missing side length of 4 units.
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The first and second shapes are rectangles.

• First we need to add the missing side lengths e.g. 4 + 4 = 8.
• We then subtract this from the perimeter e.g. 20 - 8 = 12.
• We then divide this by two e.g. 12 ÷ 2 = 6.
• This is the answer: the two missing side lengths are 6 units each.
The other two shapes just had one missing side length.
• First we add up the given side lengths e.g. 6 + 2 + 3 + 1 + 3 = 15.
• We then subtract this from the perimeter e.g. 18 - 15 = 3.
• This is the answer: the missing side length is 3 units.
• ### Can you find the missing side lengths of these items?

Hints

Start by adding up all of the known side lengths.

Subtract the total of the known side lengths from the perimeter.

What you are left with is the answer if you are looking for one missing side length.

If the shape is a rectangle and you are looking for two missing side lengths, you need to divide by two.

Solution

Van door

• The missing side length was 4 units.
• 5 + 5 + 4 + 1 + 1 = 16
• 20 - 16 = 4
Pizza box
• The missing side lengths were 5 units each.
• 6 + 6 = 12
• 22 - 12 = 10
• 10÷ 2 = 5
Desk top
• The missing side length was 4 units.
• 9 + 6 + 3 + 6 + 2 = 26
• 30 - 26 = 4
Mirror
• The missing side length was 2 units.
• 2 + 2 + 2 + 2 + 2 = 10
• 12 - 10 = 2
Clock
• The missing side length was 3 units.
• 2 + 2 + 2 + 3 = 9
• 12 - 9 = 3
Book
• The missing side lengths were 2 units each.
• 3 + 3 = 6
• 10 - 6 = 4
• 4÷ 2 = 2

• ### What is the missing side length?

Hints

Add up the given side lengths and subtract the answer from the perimeter.

5 + 2 + 2 + 3 + 3 = 15

20 - 15 = ?

Solution

The missing side length is 5 units.

5 + 2 + 2 + 3 + 3 = 15. 20 - 15 = 5

We can check our answer too: 5 + 5 + 2 + 2 + 3 + 3 = 20

• ### What is the perimeter of the climbing wall?

Hints

Work out the individual missing side lengths using the method you have been using.

• Add up the given side lengths.
• Subtract this from the perimeter.
• If the shape is a rectangle, divide this number by two.

Remember, two sides will be stuck together. The red lines show where they will be stuck together. Do you need to count these when working out the total perimeter?

Solution

The missing side lengths from the rectangular piece were 9 units each.

• 6 + 6 = 12
• 30 - 12 = 18
• 18÷ 2 = 9
This missing side length from the other piece was 3 units.
• 6 + 2 + 2 + 2 + 4 + 2 + 5 + 7 = 30
• 33 - 30 = 3
To find the total perimeter:
• The two sides of 6 units that are next to each other would have been stuck together, so we don't count these in the final perimeter.
• So we can then add 6 + 9 + 2 + 2 + 2 + 4 + 3 + 2 + 5 + 7 + 9 = 51 units.
• We could also add 6 + 6 = 12 and add 30 + 33 = 63. We can then subtract 12 from 63 to get 51.