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Perimeter

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Basics on the topic Perimeter

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?

Let’s learn more about perimeter and how to calculate it in the following explanation.

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.

Pentagon with labelled side lengths

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:

Rectangle with labelled side lengths

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

Rectangle with perimeter equation

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.

Rectangle with perimeter of fourty

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
quadrilaterals:

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:

Triangle with labelled side lengths

Pentagon with labelled side lengths

Hexagon with labelled side lengths

Octagon with labelled side lengths

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.

Transcript Perimeter

"I can't wait for our party tonight...it's going to be so much fun!" "Agreed, but don't you think we should decorate a bit?" "Hmmm, I see your point....let's see if we can buy some lights then we can hang them around the van, umbrella, and garden!" "So how many lights will we need, Zuri?" Zuri and Freddie will have to determine the perimeter of each location in order to buy enough lights for the party. Let's help them calculate the total by "Finding Perimeter with Given Side Lengths". The perimeter is the total distance around a figure or the sum of all its sides. Finding the perimeter of any figure is simple. We add up the lengths of each side to calculate the total measure. Perimeter should always be labelled using the correct unit of measure. Let's look at Zuri and Freddie's map to determine the perimeter of, or distance around, their van. First, we look at the figure's measurements. It says the van's sides are fourteen metres, six metres, fourteen metres and six metres. Next, we will write our equation by adding all the side lengths together. Fourteen plus six, plus fourteen plus six. Then, we calculate the sum. Our total is forty! Finally, we rewrite our complete answer using the correct units: forty METRES. Zuri and Freddie will have to buy forty metres of lights to string around the perimeter of their van. Now, let's find the perimeter of the umbrella...what does each side measure? Each of the six sides measures two metres. What is our next step? We write our addition equation: two plus two plus two plus two plus two plus two. Next, we add. What is the sum? The sum is twelve! What is our final step? The last step is to rewrite our complete answer using the correct units: twelve METRES. Zuri and Freddie will have to buy twelve metres of lights to string around the perimeter of their umbrella. Lastly, let's look at the garden on the map. It says the different sides measure ten metres, five metres, eight metres, five metres and ten metres. What is our first step? We write our addition equation: ten plus five plus eight plus five plus ten. What is the sum? The sum is thirty-eight! What is our final step? We rewrite the sum with the correct units next to our answer: THIRTY-EIGHT metres. Zuri and Freddie will have to buy thirty-eight metres of lights to string around the perimeter of their garden. Remember, Zuri and Freddie want to buy string lights for each location, so we need to add up EACH of the perimeters. Let's add forty plus twelve plus thirty-eight. Forty plus twelve plus thirty eight equals ninety. They will need to buy ninety metres of lights to have enough decorations. "I can't believe they had THAT many lights!" Before we see how it all turned out, let's remember how they calculated the perimeters in the first place! First, identify the side lengths of the figure. Then, write an addition equation by adding up the measurements. Next, calculate the sum. Lastly, rewrite the sum with the correct units next to the perimeter. "Do you think its too much?" "Not. A. Chance." "Yeah, it's perfect....no one will notice the rubbish now."

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.
    2. Write an addition equation by adding up the measurements.
    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.