The perimeter of a shape is the measurement of the length of the shape’s outline. If you are wondering how to measure the perimeter, add the length of all its edges.
Children might be given the perimeter of a shape and asked to work out the length of unlabelled edges.
An analogy about walking around a shape or building a fence around a field may help children to visualize this new term and understand the perimeters of shapes and how to measure perimeter.
Children can often be asked to work out the perimeter of a shape during primary school by finding the lengths of edges that haven’t been labeled using the information given.
Read on to find out:
- a step-by-step guide on how to find the perimeter of different shapes;
- the national curriculum aims regarding the perimeters of shapes, which pupils must meet;
- handy resources to support teaching about perimeter for teachers as well as parents.
Why would we measure the perimeters of shapes?
As in the example above, we teach how to measure the perimeter of 2D shapes in school. It is an essential skill taught in the maths topic of shapes and measuring areas.
Perimeter is also often used when measuring the area of a space, such as a garden or a room in your home. For example, if you want a new carpet or garden fence, you’d know the distance around your living room or garden.
So, calculating the distance around a shape or space is a useful life skill. Moreover, it is an excellent example of how maths is applied to real-life situations!
How to measure the Perimeter of Shapes?
Calculating the perimeter would depend on the shape you’ve got. However, if you have a shape with straight sides, you can follow two simple steps:
- First, find the length of each edge of the shape or space.
- Once you’ve found the lengths, you add the lengths of all the sides together to find the perimeter.
Now, let’s look at some examples of how to measure the perimeter for common 2D shapes.
How to work out the perimeter of a square?
A square is probably the most exact shape to work out the perimeter. Made up of 4 sides of equal length, a square’s perimeter can be calculated using the formula P = 4a. If it’s too early in the morning for equations, the perimeter equals 4 x the length of one side of the square.
Still not sure how to work out the perimeter of a square? Let’s look at some examples to make it a bit clearer.
Take a square with sides of 3cm; the perimeter of that shape would be the distance all around the outside of the shape. We can work this out by adding each 3 cm side (3 cm + 3 cm + 3 cm + 3 cm = 12 cm). As all the sides are the same length, we could simplify this by doing multiplication instead of repeated addition. It would look like 3 cm x 4 = 12 cm.
For a square with sides of 10 m each, the perimeter would be 40 m (10 m × 4 = 40 m).
For a square with sides of 2.5 km, the perimeter would be 10 km (2.5 km x 4 = 10 km).
Calculating the Perimeter of a Triangle
In the example below, the length of each three sides of the triangle equals 5 cm. To calculate the distance around it, you add the lengths together, resulting in a perimeter of 15 cm.
For an equilateral triangle (where all sides are the same length), you could multiply the length of one side by 3. It does not work for scalene or isosceles triangles, so watch out!
How to Find the Perimeter of a Trapezium
A trapezium is a quadrilateral shape with one pair of parallel sides. The formula for finding the perimeter of a trapezium is:
Perimeter = sum of parallel sides + sum of oblique sides
So, to find the perimeter of a trapezium, we must first find the measurement of all its parallel and oblique sides. Another way to put the formula for finding the perimeter of a trapezium is:
Perimeter = a + b + c + d
A, b, c, and d are all sides in the formula above.
Let’s go through an example:
Find the perimeter of this trapezium, where the measurements of the sides are:
- Side a: 10 cm
- Side b: 15 cm
- Side c: 8 cm
- Side d: 17 cm
So, let’s put these values into our formula.
Perimeter = a + b + c + d
Perimeter = 10 + 15 + 8 + 17
Perimeter = 50 cm
Finding the perimeter for a trapezium is pretty simple, as it is just a process of addition. However, practice makes perfect, so let’s go through another example.
Find the perimeter of this trapezium, where the measurements of the sides are:
- Side a: 30 cm
- Side b: 55 cm
- Side c: 29 cm
- Side d: 37 cm
So, let’s put these values into our formula.
Perimeter = a + b + c + d
Perimeter = 30 + 55 + 29 + 37
Perimeter = 151 cm
Find the Perimeter of a Parallelogram
When asking ‘How to find the perimeter of a parallelogram, we must find the sum of all the edges of the shape. However, we can make our calculations easier because rectangles and parallelograms have two pairs of equal parallel sides.
Children will be introduced to two methods for how to find the perimeter of a parallelogram. We will use both ways so that you can work out the perimeter in this case. But first, let’s have a look at the example below.
- The first method is to add all the lengths of the sides, which would show that the perimeter of the rectangle above is 28 cm.
10 cm + 10 cm + 4 cm + 4 cm = 28 cm
- The second method considers that rectangles have two pairs of equal, parallel sides. So, you can multiply 10 cm by 2 and 4 cm by 2 and add the totals together.
10 × 2 + 4 × 2 = 20 + 8 = 28 cm
Children will reach the same answer using either of the two methods above. So this is an excellent way of showing them how to find the perimeter of a parallelogram and how interconnected geometry and maths calculations are.
Finding the Perimeter of a Rectilinear Shape
Even though rectilinear shapes might seem confusing initially, children must follow the same two steps to calculate the distance around these shapes.
In the example below, the lengths of all sides are given, so all you must do is add them up.
Sometimes, however, pupils must calculate the length of any sides not given – see the rectilinear shape below.
In this case, you can work out the length of side a by adding the ones opposite it: 3 and 6.
a = 3 cm + 6 cm = 9 cm
You’ll notice that side b can be found by subtracting 7 from 10.
b = 10 cm – 7 cm = 3 cm
So, now that you know the lengths of all sides, you can calculate the perimeter by adding them together.
10 cm + 3 cm + 3 cm + 6 cm + 7 cm + 9 cm = 38 cm
Finding the Perimeter of a Circle
Circles are different, as they don’t have straight sides. But of course, we can still find the distance around them.
Children will learn that the perimeter of a circle is also called ‘the circumference.’ Because measuring the distance around this shape is difficult, a formula is followed to calculate the circumference.
Here’s the formula with an explanation of what each symbol stands for:
C = 2πr
C = circumference, π (pi) = a constant, which is approximately 3.14, r = radius
See the image below for an example of how it’s calculated.
How to find the perimeter of an irregular shape?
If a shape is irregular, the sides are not all the same length. To find the perimeter, you must add up all the lengths of its outer sides. Ensure to include the correct unit in your answer.
How To Work out Perimeter: Quick Fire Formulas
When teaching kids how to work out the perimeter of shapes, it can be handy to have a list of the different formulas on hand. Depending on what level they are working at, many of these formulas will not apply to kids as they are too advanced. However, they are still good to keep a note of for later learning.
The formula for a parallelogram is:
2(Base + Height)
The formula for a triangle is:
a + b + c
In this formula, a, b and c represent the side lengths of the shape.
The formula for a rectangle is:
2(Length + Width)
The formula for a square is:
4a
In this formula, a represents the length of a side.
The formula for a trapezoid is:
a + b + c + d
In this formula, a, b, c, and d represent the four sides of the trapezoid.
The formula for a kite is:
2a + 2b
In this formula, a represents the length of the first pair, and b represents the length of the second pair.
The formula for a rhombus is:
4 x a
In this formula, a represents the length of a side.
The formula for a hexagon is:
6 x a
In this formula, a represents the length of a side.
What’s the difference between perimeter and area?
Pupils will learn about area and perimeter usually around the same time, so it’s essential to know the difference between them.
As mentioned above, a perimeter is a distance around the outside of a shape. On the other hand, the area is the amount of space inside a shape. See the visual aid below, which shows the difference between the two.
Finding the perimeter in real life
You can find the perimeter of almost any object in real life. The same principles as what you’ve done on paper apply similarly. Here’s a step-by-step guide on how to measure something’s perimeter. Just remember, you might not be able to measure everything.
- The first step is to decide what to measure the perimeter of. Usually, 3D objects don’t have a perimeter, but we’re not going to measure all of the objects.
- Let’s say you want to measure a fridge. That’s an excellent way to practice your perimeter skills. So, pick a side you want to measure the perimeter of.
- So, you’ve picked the front? Excellent! That’s even better if your fridge has two doors; it’s double the practice.
- First, you must measure all sides of the fridge’s front. If it has two doors, measure them separately so you can do twice the practice.
- After you’ve got the measurements, you can do the calculation to work out the perimeter. Remember, add all the numbers up and ensure they’re the same unit!
