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Rectilinear shapes: how to find their area and perimeter

What exactly are rectilinear shapes, and how do you find their area and perimeter? With a few tips in hand, it’s easy to get to grips with them. Take a look at our handy guide below!

In this blog, you’ll find:

  • What is a rectilinear shape?
  • Examples of rectilinear shapes
  • How to find the perimeter of rectilinear shapes
  • How to find the area of rectilinear shapes

What is a rectilinear shape?

A rectilinear shape is a 2D, flat shape that has straight sides. All of the sides meet at right angles (angles that are 90 degrees). The outline of the shape is a single line from start to finish.

Rectilinear shapes are sometimes known as composite rectilinear shapes because they are a 2D shape made up of other 2D shapes. A rectilinear shape often looks like two or more rectangles put together to form one shape — think of them as the shape version of a Transformer!

Usually, children first look at rectilinear shapes in Year 4, where they begin to understand them through the use of squares.


Examples of rectilinear shapes

Rectilinear shapes can look very different, but they all have straight lines and right angles.

The most basic rectilinear shape looks like two rectangles sitting against each other.

Others can be lots of small rectangles put together and piled on top of each other, making the shape look like steps.

Some special rectilinear shapes even look like ancient Mayan pyramids! You can almost imagine yourself climbing up the side of them.


How to find the perimeter of rectilinear shapes

A rectilinear shape can look very complicated, but don’t worry – working out its perimeter is exactly the same as working out the perimeter of a rectangle.

To work out the perimeter of rectilinear shapes, all you have to do is add the length of each side together. Let’s take a look at some examples to get you started:

This basic rectilinear shape below has 6 different sides. To find the perimeter, simply add the length of each side together.

Remember to include a label for your units. In this case, as the sides are in centimetres, the final unit will be in cm. Be careful of this, as some questions may as you to work out a shape in metres too!

This would be 14 + 5 + 7 + 7 + 3 + 8 = 44cm.

Now let’s look at a trickier question. Take a look at the rectilinear shape below. You’ll probably notice that there are some sides without a measurement. Don’t worry — there’s an easy way to work this out.

Your first step will be to work out what length the missing sides of the shape are. Let’s start with the vertical line first that we’ve labelled ‘a’.

On the opposite side of the shape, we can see that the two lengths are 5cm and 2cm. To find side a, all you have to do is add these two lengths together.

5cm + 2cm = 7cm, so side ‘a’ measures 7cm.

Now let’s focus on the horizontal line that we do not have a measurement for – line ‘b’. You can see that the longest horizontal length measures 9cm, and line b and the 6cm line add up to be the same length as this.

Therefore, to work out the length of line ‘b’, we need to take 6cm away from 9cm.

9cm – 6cm = 3cm, so side ‘b’ measures 3cm.

Now that we have all of the line lengths, they just need to be added together to work out the perimeter, like in our previous example.

6 + 3 + 5 + 2 + 9 + 7 = 32cm.

Therefore, the total perimeter of the rectilinear shape above is 32cm!

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How to find the area of rectilinear shapes

Once children understand how to work out the perimeter of a rectilinear shape, they can move on to working out the area. Again, this is very similar to working out the area of a rectangle, as a rectilinear shape can be broken down into smaller rectangles.

Let’s remind ourselves how to work out the area of a simple rectangle. To find the area of a rectangle, simply multiply the length of the longer side by the length of the shorter side.

For example, for the rectangle below, the calculation would be: 3 x 12 = 36cm2

As we’re working with area, it’s important that the units are cm2 (centimetres squared).

Now, let’s take a look at how we can use this knowledge to work out the area of rectilinear shapes. For children that are beginners to this, the easiest way to help their understanding of area is to have the shapes on centimetre squared paper, like in the example below.

As the shape is already on centimetre paper, children can simply start by counting the boxes to find out the total area. As you can see from the diagram above, the total number of squares is 22, meaning that the area is 22cm2.

Once children have grasped the concept of area, you can now move on to calculating it through the lengths of the sides. Take a look at the shape again…

You can see that this composite rectilinear shape is made up of two rectangles. To work out the area, calculate the area of each rectangle separately and then add them together. The above shape can be broken down into the two rectangles below.

Once you have broken the rectilinear shape down, you first need to work out the area of the first rectangle:

4 x 3 = 12cm2

Then, work out the area of the second rectangle:

5 x 2 = 10cm2

To find the area of the shape overall, you simply add these two areas together…

10 + 12 = 22 cm2

So the area of this rectilinear shape is 22cm2!


The take away

Rectilinear shapes can look strange at first, but there’s nothing to fear! Once children understand that they are just like smaller rectangles put together, working out the area and perimeter can be learned with practice and a few handy rules to keep in mind.

Looking for more ways to explore rectilinear shapes? Download DoodleMaths today to enjoy thousands of personalised exercises tailored to your child’s needs!

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