“What is the Perimeter?” – It’s good to understand the definition of primary school maths concepts before trying to explain with an example. The perimeter of a shape is the total of the length of the outside edge of the shape. It can be found by adding up the lengths of all the individual edges.

What is the perimeter?

At a KS2 primary school maths level, we can think of the perimeter a bit like a path, if you were to walk around a shape, following every edge completely, and taking measurements as you go, the total of these measurements would be the perimeter.

Let’s think about some examples to help you and your kids find the perimeter. These will help it make more sense! At the end of this blog you can also find some KS2 SATs perimeter questions. These will be around the topics of ‘Year 5 finding the perimeter’ and ‘Year 6 finding the perimeter’.

So now that you know what the perimeter is, let’s visualise it:

A useful way to think about perimeter and other concepts in KS2 maths is a real-life example, this often helps both teachers and learners to visualise the concept. Let’s imagine an example of a park with one entrance and one exit. This park has a path which covers the complete area of the park going along the outside edge.

Measuring the perimeter in this case will tell us the length of this path. Now we know how to think about perimeter in some real-life examples, we can move onto some math examples. Using visual stimuli and graphics is a key bonus of primary school maths online.

How do you teach kids about the perimeter?

Teaching kids about perimeter can be confusing, as well as the visualisation and real-life comparison techniques explained above, you can use common shape examples. Questions can involve both simple and complex shapes. A good method is to understand the perimeters of simple shapes, so that you can then use this to break down and work out more difficult questions. It can also be useful to draw shapes out and use measuring instruments and stationery to help students find the perimeter. Get out the rulers of all shapes and sizes and get kids to start measuring the sides of shapes themselves and adding up the units on a ruler!

How to find the perimeter of a triangle:

We know that a triangle is a three-sided shape, so the perimeter will be found by simply adding up the lengths of these three sides. Let’s consider the triangle in the image below;

We can clearly see the three sides of this shape, and their labelled measurements. To find the perimeter, all we need to do is add up these lengths. So, in this case the perimeter of this shape would be:

Perimeter = 3cm + 5cm + 5cm = 13cm

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How to find the perimeter of a square:

We can again see the four sides, each with their labelled edge length. As we have said, this is a square so all the sides have the same length.
Now, let’s think about finding the perimeter of a square. Whilst a square has one more side than a triangle, finding the perimeter can actually be easier. This is because, we know that in a square, all the sides are of equal length. So, let’s think about the square pictured below;

Perimeter = 6cm + 6cm + 6cm + 6cm = 4x6cm = 24 cm

It follows from this that to work out the perimeter of a square, you simply need to know one side length, then times this by 4, and you have worked out the perimeter! This will be a common question in early KS2 Maths, but for Year 5 and 6 primary school maths it will usually be a little more complex. Nevertheless, it’s always important to know these formulas as it may still be a part of a more complex KS2 SATs perimeter question.

How to find the perimeter of a rectangle?

Here is another instance of these KS2 maths questions bringing in more real-life examples. You will often find that questions relate to a real-life scenario or object, this can often be something like a sports field or a swimming pool, and in these two specific examples you will often find rectangles, let’s call these approaches (a) and (b). Sometimes these questions will be presented as below; in style (a)

In this example (a), just like in the instance of the square and triangle, you are given the lengths of all four sides, and simply need to add this up, i.e. the perimeter of the rectangular swimming pool pictured is;

Perimeter = 10m + 10m + 6m + 6m = 32m

However, there is another way that you can find this question, in this way (b) you would only be given two sides. Like this example;

Answering this relies on the primary school student’s understanding of shapes, so they must notice that this is a rectangle and therefore that the two sides not given can be found. I.e. in a rectangle you always have that the two parallel sides are of equal length. Hence, from an example like this; the longer side not given will also be 12m and the shorter will be 5m.

Hence the perimeter of this rectangle can be worked out as;

Perimeter = 12m + 5m + 12m + 5m = 34m

How to find the perimeter of a circle

Now moving to a circle, this is slightly different, as we know a circle has no straight edges, so we have to use a different method. The way we work this out for KS2 maths level is by using a simple formular that we have to remember. The perimeter of a circle = 2 x π x r = 2πr, where π is the mathematical constant of pi and r is the radius of the circle.

Let’s see an example;

As we can see in the question, we must know the radius of the circle to find out the perimeter. The radius is simply half of the diameter.

So, in this example, we can see that the Radius of the circle is given as 3, we can now simply use the formular 2πr, with the value of r to be 3.

Perimeter = 2 x π x 3 = 6π or 18.84956….

What is the circumference of a circle?

Now you may see the word circumference of a circle coming up in KS2 primary school math questions. The circumference of a circle is the perimeter, simple as! They mean the same thing. So, working out the circumference of a circle uses exactly the same method as above. Easy!

Perimeter of a circle = Circumference

How to find the perimeter of a polygon?

Remembering general formular for helping your year 5 or 6 student find the perimeter of a polygon is a helpful way to keep on top of things. Firstly, a reminder – a polygon is any shape with more than three sides, and straight edges, i.e. one that can be drawn on a flat surface.

For a regular polygon, i.e. every side is the same length, the perimeter is given by;

Perimeter = length of one side x the number of sides

For an irregular polygon, i.e. the sides are not all the same length, the perimeter is given by;

Perimeter = the sum of all of the side length

Are area and perimeter the same?

No! It’s important to remember the difference between area and perimeter as they will often be featured together in questions. A good way to think about the difference between these two concepts is the inside and outside. The perimeter of a shape is the measurement of the outside of it, as we have seen, the path around the shape. Whereas, the area of a shape is the measurement of everything inside the shape. Another key difference is the unit, area will be measured in ‘units squared’ whereas perimeter will be measured in just the units. I.e. you may find the area of a shape to be 3 meters squared, but the perimeter of a shape to be 3 meters. Visually, the picture below helps us to understand this. 

The area of these two shapes is found by counting up the squares inside the shapes – i.e. the part in red. The perimeter of these shapes is given by the black line surrounding the shape edge.

A brain teaser question

Here, we are given a rectangular piece of wood. The PERIMETER of this piece of wood is 14m, and we are given that the longest side measures 5m. Can you work out the lengths of the other sides?

Combining Shapes

A lot of KS2 primary school maths questions will involve combined shapes, sometimes giving you just one or two lengths, so you must 1) work out what the lengths of the other sides are, and 2) work out what the overall perimeter is. Here’s an example.

In this question we have 6 equilateral triangles of 2 different sizes. These one’s are coloured in differently so we can tell, but it could be the case that they aren’t separated this obviously.

We are only told that the length of the smaller equilateral triangle is side is 2cm (remember equilateral means all the sides are of equal length). So, let’s see what we notice from the picture;

• The side of the larger triangle = 3 of the sides of the smaller triangle. I.e. the side of the larger triangle is therefore 6cm.
• The bottom of the shape is made up of 2 sides of the smaller triangle, i.e. = 4cm.
• There are 2 green sides = 2 x 2cm.
• The outside has also got 2 sides of the blue triangle. I.e. 6cm x 2.
• So now, we want to add all of these sides together:

Perimeter = 6cm + 6cm + 2cm + 2cm + 4cm

KS2 perimeter worksheets and practice questions

KS2 perimeter worksheets and practice questions – answers

• 299m
• 54
• E
• 80

1 mark for correct calculation; (13 + (12-5)) x 4.

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Parents use our online maths tutors as a supplement to the learning that takes place at school. With multiple difficulty levels, all our online maths courses use a state-of-the-art online learning platform pioneering the UK’s first dual-teacher system. This creates a comprehensive, guided-learning experience suitable for every child, enabling them to catch up and make progress in maths.  

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