Perimeter

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Finding Perimeter with Given Side Lengths

It is summer time and in order to make summer evenings even better, your family wants to decorate the space around your pool with lights. However, you will need to determine the perimeter of the pool in order to buy enough lights to string around the edges. This key stage two video and text teaches you how to find the perimeter of a shape with given side lengths. Continue reading if you want to learn how to work out perimeter.

What Is Perimeter?

What Does Perimeter Mean?

The perimeter meaning is the total distance around a figure, or the sum of all its sides. Finding the perimeter of any shape, regular or irregular, is simple: add up the lengths of each side to work out perimeter. The perimeter is always labelled using the correct unit of measure. Common units for perimeter might be centimetres, metres, kilometres, inches, feet, yards and miles.

Perimeter vs. Circumference

Circumference is a special name given to a circle’s perimeter. However, finding the circumference requires a special perimeter formula. It is not just adding side lengths.

How to Calculate Perimeter

The perimeter equals the sum of all of a figure's side lengths. When working out perimeter, begin by looking at the shape’s side measurements. For our pool, the sides are labelled fourteen metres, six metres, fourteen metres and six metres:

Next, write the perimeter equation by adding all of the side lengths together: 14 + 6 + 14 + 6:

Then, determine the perimeter by calculating the sum and labelling with correct units. The solution to this perimeter problem is 40 metres. This means, we need to buy 40 metres of string lights for the pool area.

How to Work Out the Perimeter of a Shape – Formulas and Examples

In the table below are several polygon perimeter examples.

Polygon Perimeter
triangle side 1 + side 2 + side 3

square, rectangle, parallelogram, trapezium, rhombus
side 1 + side 2 + side 3 + side 4
pentagon side 1 + side 2 + side 3 + side 4 + side 5
hexagon side 1 + side 2 + side 3 + side 4 + side 5 + side 6
octagon side 1 + side 2 + side 3 + side 4+ side 5 + side 6 + side 7 + side 8

For a better visual illustration, the following infographics show the perimeters of a triangle, pentagon, a hexagon and an octagon:

How to Measure Perimeter – Summary of Steps

• First, look at the figure's side measurements.

• Next, write the perimeter equation by adding all of the side lengths together.

• Then, determine the perimeter by calculating the sum.

• Finally, label the answer with correct units.

Have you practised perimeter questions yet? On this website, you can also find perimeter worksheets and exercises.

Perimeter exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Perimeter.
• What is the perimeter of the garden?

Hints

Remember, the perimeter is the distance around the shape. It is the total length of all of the shape's sides.

As an example, this is how you would find the perimeter for the rectangle below.

Solution

The perimeter of a shape is the distance around the shape.
To find the perimeter, we must find the sum of the shape's sides by adding.

10 + 15 + 10 + 15 = 50
The perimeter of the garden is 50 metres.

• How do you find the perimeter of a shape?

Hints

Looking at the picture of the rectangle, what is the first step we need to take to find the perimeter?

To find the perimeter, you must add the lengths of all sides of the shape.

Remember it is important to include the measurement units!

Solution

Perimeter is the distance around an object. To find the perimeter you must:

1. Identify the side lengths and units of the figure.
3. Add by calculating the sum of the sides.
4. Rewrite the sum with the correct units next to the perimeter.
• What is the perimeter of each shape?

Hints

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides. To find the perimeter, find the total length of the shape's sides.

As an example, this is how you would find the perimeter for the shape below.

Solution

Perimeter is the distance around a shape. To find the perimeter, find the total length of the shape's sides.

Rectangle: 7 + 20 + 7 + 20 = 54
The perimeter of the rectangle is 54 cm.

Triangle: 15 + 15 + 15 = 45
The perimeter of the triangle is 45 cm.

Square: 12 + 12 + 12 + 12 = 48
The perimeter of the square is 48 cm.

Parallelogram: 13 + 13 + 13 + 13 = 52
The perimeter of the parallelogram is 52 cm.

• What is the perimeter of each window?

Hints

The perimeter of a shape is the distance around the shape.

Add the lengths of the sides to find the total distance around the shape.

As an example, this is how you would find the perimeter for the shape below.

Solution

The perimeter of a shape is the distance around the shape. To find the perimeter, find the total length of the shape's sides.

Window 1:
16 + 12 + 14 + 18 = 60
The perimeter of window 1 is 60 cm.

Window 2:
14 + 28 + 14 + 28 = 84
The perimeter of window 2 is 84 cm.

Window 3:
14 + 22 + 18 + 28 = 82
The perimeter of window 3 is 82 cm.

• What is the perimeter of the pentagon?

Hints

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

To calculate the perimeter, you must find the sum of the shape's sides. As an example, this is how you would find the perimeter for the shape below.

Solution

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

To find the perimeter, add the lengths of each side of the pentagon.

3 + 3 + 3 + 3 + 3 = 15

The perimeter of the pentagon is 15 centimetres.

• Which shapes have a perimeter of 24 centimetres?

Hints

More than one shape has a perimeter of 24 centimetres.

Perimeter is the distance around a shape. As an example, this is how you would find the perimeter for the rectangle below.

Solution

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

To find the perimeter:

1. Identify the side lengths and labels.
2. Add to find the sum which is the perimeter of the shape.

Square:
6 + 6 + 6 + 6 = 24
The perimeter of the square is 24 cm.

Rectangle:
3 + 9 + 3 + 9 = 24
The perimeter of the rectangle is 24 cm.

Pentagon:
5 + 5 + 5 + 5 + 5 = 25
The perimeter of the pentagon is NOT 24 cm.

Triangle:
8 + 8 + 8 = 24
The perimeter of the triangle is 24 cm.