How to work out perimeter

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Arithmetic Decimals Fractions 2D shapes

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GCSE Maths Geometry and Measure 2D Shapes

How To Work Out Perimeter

Here we will learn how to work out perimeter, including what the perimeter of a shape is and how to calculate it for different shapes. We will also look at perimeter word problems.

There are also how to work out perimeter 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 working out perimeter?

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

For example,

Calculate the perimeter of the triangle.

\text{Perimeter}=5+12+13=30 \ \text{cm}

Step-by-step guide: Perimeter of compound shapes

What is working out perimeter?

Perimeter of rectangles

The opposite sides of a rectangle are equal, $a$ and $b$ are the side lengths.

The perimeter of the rectangle is

\text{Perimeter}=a+b+a+b=2a+2b \ \text{or} \ 2(a+b)

Perimeter of circles

The perimeter of a circle is known as the circumference of a circle.

\text{Circumference} = \pi \times d = 2 \times \pi \times r

Step-by-step guide: Circumference of a circle

Perimeters of triangles and quadrilaterals

We can calculate the perimeter of any polygon (2D shape) by adding together the lengths of all the sides.

For example, calculate the perimeter of the triangle. All measurements are in cm.

\text{Perimeter}= 25 + 25 + 14 = 64 cm

Calculate the perimeter of the trapezium. All measurements are in cm.

\text{Perimeter} = 10 + 14 + 10 + 30 = 64 cm

For example, calculate the perimeter of the parallelogram. All measurements are in cm.

\text{Perimeter} = 8 + 4 + 8 + 4 = 24 cm

How to work out the perimeter

In order to work out the perimeter of a shape:

Add all the side lengths.
Write the final answer with the correct units.

How to work out the perimeter

How to work out the perimeter worksheet

Get your free how to work out the perimeter worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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How to work out the perimeter worksheet

Get your free how to work out the perimeter worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

How to work out perimeter examples

Example 1: irregular shape

Find the perimeter of this triangle.

Add all the side lengths.

16+6+11=33

2Write the final answer with the correct units.

The correct units for this question are centimetres.

The perimeter is $33 \; cm$

Example 2: irregular shape

Find the perimeter of this quadrilateral.

Add all the side lengths.

Add the side lengths together. Make sure that you get each side.

$8+5+6+5=24$

Write the final answer with the correct units.

The correct units for this question are centimetres.

The perimeter is $24 \; cm$ .

Example 3: rectangle

Find the perimeter of this rectangle.

Add all the side lengths.

Add the side lengths together. Remember that the opposite sides of a rectangle are equal.

$7+2+7+2=18$

Alternatively, we can use a perimeter formula to find the perimeter of a rectangle.

$\text{Perimeter}=2a+2b=2\times 7+2\times 2=14+4=18$

$\text{Perimeter}=2(a+b)=2(7+2)=2\times 9=18$

Write the final answer with the correct units.

The correct units for this question are centimetres.

The perimeter is $18 \; cm$ .

Example 4: rectangle

Find the perimeter of this rectangle.

Add all the side lengths.

Add the side lengths together. Remember that the opposite sides of a rectangle are equal.

$5.1+9.4+5.1+9.4=29$

Alternatively, we can use a perimeter formula to find the perimeter of a rectangle.

$\text{Perimeter}=2a+2b=2\times 5.1+2\times 9.4=10.2+18.8=29$

$\text{Perimeter}=2(a+b)=2(5.1+9.4)=2\times 14.5=29$

Write the final answer with the correct units.

The correct units for this question are centimetres.

The perimeter is $29 \; cm$ .

Example 5: regular polygon

Find the perimeter of this square.

Add all the side lengths.

Add the side lengths together. Remember that all the sides of a regular shape such as a square are equal.

$3.7+3.7+3.7+3.7=14.8$

Alternatively, we can multiply the number of sides by the side length.

$4\times 3.7=14.8$

Write the final answer with the correct units.

The correct units for this question are centimetres.

The perimeter is $14.8 \; cm$ .

Example 6: regular polygon

Find the perimeter of this regular hexagon.

Add all the side lengths.

Add the side lengths together. Remember that all the sides of a regular shape such as a square are equal.

$8.2+8.2+8.2+8.2+8.2+8.2=49.2$

Alternatively, we can multiply the number of sides by the side length.

$6\times 8.2=49.2$

Write the final answer with the correct units.

The correct units for this question are millimetres.

The perimeter is $49.2 \; mm$ .

How to solve word problems involving perimeter

In order to solve word problems involving perimeter:

Consider the shape in the question and how to find its perimeter.
Work out the missing side.

Example 7: word problems

A triangle has a perimeter of $18 \; cm.$

Two of its sides are $7 \; cm.$

Find the missing side.

Consider the shape in the question and how to find its perimeter.

The shape is a triangle.

To find the perimeter of a triangle we find the sum of the lengths.

Work out the missing side.

We can work out the missing side by subtracting the two sides in the question from the perimeter.

$18-(7+7)=18-14=4$

The missing side is $4 \; cm$ .

Example 8: word problems

A rectangle has a perimeter of $21 \; cm.$

The shortest side is $4 \; cm.$

Find the length of the longest side.

Consider the shape in the question and how to find its perimeter.

The shape is a rectangle.

The formula for finding the perimeter of a rectangle is,

$\text{Perimeter}=2(a+b)$ .

Work out the missing side.

We can work out the missing side by dividing the perimeter by $2$ , and then subtracting the side length given in the question.

$(21\div 2)-4=10.5-4=6.5$

The longest side is $6.5 \; cm$ .

Alternatively you can rearrange the perimeter formula.

$\begin{aligned} \text{Perimeter}&=2(a+b)\\\\ 2(a+4)&=21 \\\\ a+4&= 10.5\\\\ a&=6.5 \end{aligned}$

Common misconceptions

Order of adding the sides

It doesn’t matter the order in which the sides of the shape are added.

Check the units

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

Practice how to work out perimeter questions

19.2 \; cm

19.3 \; cm

19.1 \; cm

19.4 \; cm

Adding up all the side lengths gives

$7.1+6.9+5.3=19.3 \ \text{cm}$ .

26.9 \; cm

21.4 \; cm

21.2 \; cm

26.88 \; cm

Adding up the short and long side and then doubling gives

$2\times (6.4+4.2)=2\times 10.6=21.2 \ \text{cm}$ .

36.4 \; mm

36.6 \; mm

36.7 \; mm

36.5 \; mm

For a regular polygon we can multiply the length of one side by the number of sides,

$5\times 7.3=36.5 \ \text{mm}$ .

4.3 \; cm

4.2 \; cm

4.1 \; cm

4.5 \; cm

Subtracting the side lengths from the perimeter gives

$21.6-(8.1+9.2)=21.6-17.3=4.3 \ \text{cm}$ .

12.9 \; mm

12.8 \; mm

12.7 \; mm

12.6 \; mm

Dividing the perimeter by $2$ and then subtract the given side,

$(35.6\div 2)-4.9=12.9 \ \text{mm}$ .

3.7 \; mm

3.6 \; mm

3.5 \; mm

3.4 \; mm

Dividing the perimeter by the number of sides gives

$29.6\div 8=3.7 \ \text{mm}$ .

How to work out perimeter GCSE questions

1. The perimeter of a square is $36 \; cm.$

What is the side length of the square?

Circle the correct answer.

\begin{aligned} &\text{A} \quad \quad \quad \quad \text{B} \quad \quad \quad \quad \text{C} \quad \quad \quad \quad \text{D} \\ &6 \; cm \quad \quad 9 \; cm \quad \quad \;\; 4 \; cm \quad \quad \;\; 12 \; cm \end{aligned}

(1 mark)

Show answer

\text{B}-9 cm

(1)

2. A shape is formed from a rectangle measuring $11 \; cm$ by $14 \; cm$ from which a rectangle of length $7.1 \; cm$ has been removed.

How to work out perimeter GCSE Question 2

Find the perimeter of the shape.

(3 marks)

Show answer

14-4.8-5.9=3.3

(1)

11+14+11+5.9+7.1+3.3+4.8

(1)

64.2

(1)

3. The diagram shows a regular hexagon and a rectangle.

How to work out perimeter GCSE Question 3 Image 1

The perimeter of the regular hexagon is the same as the perimeter of the rectangle.

The length of the rectangle is $9 \; cm.$

Work out the width of the rectangle.

(3 marks)

Show answer

6\times 5=30

(1)

(30\div 2)-9

(1)

6

(1)

Learning checklist

You have now learned how to:

Work out the perimeter of irregular geometric shapes

Work out the perimeter of a rectangle

Work out the perimeter of a regular polygon

Problem solve involving perimeter

The next lessons are

Still stuck?

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