Perimeter Of Compound Shapes

Here we will learn about the perimeter of compound shapes, including how to find the perimeter of compound shapes.

There are also perimeter of compound shapes 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 perimeter of compound shapes?

Perimeter of compound shapes is the distance around a compound shape. 

The perimeter of a shape is finding the total distance around the outside of a 2D shape.

A compound shape (or composite shape) is any shape which is made up of two or more shapes. They are often rectilinear shapes which have straight sides and right angles. 

For example,

Find the perimeter of this compound shape.

Perimeter Of Compound Shapes image 1

To find the perimeter we add all the lengths of the sides.

3+2+4+3+7+5=24

The perimeter is 24 \ cm.

What is perimeter of compound shapes?

What is perimeter of compound shapes?

How to calculate the perimeter of compound shapes

In order to calculate the perimeter of compound shape:

  1. Work out any missing lengths.
  2. Add all the side lengths.
  3. Write the final answer with the correct units.

Explain how to calculate the perimeter of compound shapes

Explain how to calculate the perimeter of compound shapes

Perimeter of compound shapes worksheet

Perimeter of compound shapes worksheet

Perimeter of compound shapes worksheet

Get your free perimeter of compound shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Perimeter of compound shapes worksheet

Perimeter of compound shapes worksheet

Perimeter of compound shapes worksheet

Get your free perimeter of compound shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on how to work out perimeter

Perimeter of compound shapesΒ is part of our series of lessons to support revision on 2D shapes andΒ how to work out perimeter. You may find it helpful to start with the mainΒ 2D shapesΒ 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:

Perimeter of compound shapes examples

Example 1: rectilinear shapes

Calculate perimeter.

Perimeter Of Compound Shapes example 1

  1. Work out any missing lengths.

There are some missing lengths we need to work out first. We can look at the vertical lengths. The missing vertical length is 7 \ cm because 11-4=7.

Perimeter Of Compound Shapes example 1 step 1

We can then look at the missing horizontal length. The missing side is 5 \ cm because 7-2=5.

Perimeter Of Compound Shapes example 1 step 1 image 2

2Add all the side lengths.

Starting in the top left corner and going clockwise around the shape, we can add the sides together.

Perimeter Of Compound Shapes example 1 step 2

2+7+5+4+7+11=36

3Write the final answer with the correct units.

The perimeter of the compound shape is 36 \ cm.

Example 2: rectilinear shapes

Calculate perimeter.

Perimeter Of Compound Shapes example 2

Work out any missing lengths.

Add all the side lengths.

Write the final answer with the correct units.

Example 3: finding the missing side given the perimeter

The perimeter is 58.6 \ m, find x.

Perimeter Of Compound Shapes example 3

Work out any missing lengths.

Add all the side lengths.

Write the final answer with the correct units.

Common misconceptions

  • Order of adding the sides

Addition is commutative. This means it doesn’t matter what order the sides of the shape are added in.

  • Check the units

Check which units are involved in the question as there may be a mixture.

Practice perimeter of compound shapes questions

1. Find the perimeter of this 2D shape.

 

Perimeter Of Compound Shapes practice question 1

31 \ cm
GCSE Quiz False

30 \ cm
GCSE Quiz False

39 \ cm
GCSE Quiz False

38 \ cm
GCSE Quiz True

Add all the sides together.

 

Perimeter Of Compound Shapes practice question 1 explanation image

 

The perimeter is 38 \ cm because

 

4+2+7+8+11+6=38.

2. Find the perimeter of this 2D shape.

 

Perimeter Of Compound Shapes practice question 2

23 \ cm
GCSE Quiz False

25 \ cm
GCSE Quiz False

28 \ cm
GCSE Quiz True

20 \ cm
GCSE Quiz False

Add all the sides together.

 

Perimeter Of Compound Shapes practice question 2 explanation image

 

The perimeter is 28 \ cm because

 

5+1+4+3+7+8=28.

3. Find the perimeter of this 2D shape.

 

Perimeter Of Compound Shapes practice question 3

33 \ m
GCSE Quiz False

44 \ m
GCSE Quiz True

78 \ m
GCSE Quiz False

148 \ m
GCSE Quiz False

The missing sides are 5 \ m and 6 \ m.

 

Perimeter Of Compound Shapes practice question 3 explanation image

 

The perimeter is 44 \ m because

 

5+10+12+4+7+6=44.

4. Find the perimeter of this 2D shape.

 

Perimeter Of Compound Shapes practice question 4

31 \ m
GCSE Quiz False

114 \ m
GCSE Quiz False

90 \ m
GCSE Quiz False

62 \ m
GCSE Quiz True

The missing sides are 9 \ m and 22 \ m.

 

Perimeter Of Compound Shapes practice question 4 explanation image

 

The perimeter is 62 \ m because

 

9+22+3+14+6+8=62.

5. Find the perimeter of this 2D shape.

 

Perimeter Of Compound Shapes practice question 5

49 \ cm
GCSE Quiz False

270 \ cm
GCSE Quiz False

66 \ cm
GCSE Quiz False

80 \ cm
GCSE Quiz True

The missing sides are 6 \ cm , 7 \ cm and 18 \ cm.

 

Perimeter Of Compound Shapes practice question 5 explanation image

 

The perimeter is 80 \ cm because

 

6+7+6+7+3+18+15+18=80.

6. The perimeter of this 2D shape is 48 \ m. Find the value of x.

 

Perimeter Of Compound Shapes practice question 6

12
GCSE Quiz False

14
GCSE Quiz True

16
GCSE Quiz False

18
GCSE Quiz False

The missing horizontal side is 10 \ cm.

 

Perimeter Of Compound Shapes practice question 6 explanation image 1

 

The two vertical missing sides will add together to make x \ cm.

 

Perimeter Of Compound Shapes practice question 6 explanation image 2

 

The perimeter of the shape can be used to form an equation which can be solved to find x.

 

\begin{aligned} 2x+20 &= 48 \\\\ 2x &= 28 \\\\ x&=14 \end{aligned}

Perimeter of compound shapes GCSE questions

1. Calculate the perimeter of the shape below.

 

Perimeter Of Compound Shapes GCSE Question 1

 

(2 marks)

Show answer

For finding the missing sides.

 

Perimeter Of Compound Shapes GCSE Question 1 image 2

(1)

42 \ m

(1)

2. Calculate the perimeter of the shape below.

 

Perimeter Of Compound Shapes GCSE Question 2

 

(3 marks)

Show answer

For finding the missing base, 10 \ cm.

 

Perimeter Of Compound Shapes GCSE Question 2 image 2

(1)

(9 \times 2)+10+(2 \times 9)

(1)

46 \ cm

(1)

3. (a) Calculate the perimeter of the shape below.

 

Perimeter Of Compound Shapes GCSE Question 3

 

(b) A regular pentagon has the same perimeter as the shape in part a.

Find the length of one side of the regular pentagon.

 

(5 marks)

Show answer

(a)

 

45 \ mm = 4.5 \ cm \ (or 6.8 \ cm = 68 \ mm)

(1)

1.8 \ cm \ ( or 18 \ mm) and 3.1 \ cm ( or 31 \ mm).

(1)

Perimeter is 22.6 \ cm \ ( or 226 \ mm) .

(1)

 

(b)

 

22.6 \div 5 \ ( or 226 \div 5)

(1)

4.52 \ cm \ ( or 45.2 \ mm)

(1)

Learning checklist

You have now learned how to:

  • Work out the perimeter of compound shapes
  • Find the missing side of a compound shape, given its perimeter
  • Solve problems involving the perimeter of compound shapes (or composite shapes)

The next lessons are

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