- Perimeter is the total distance around the outside of a shape.
- The two green horizontalGoing from left to right across this screen.sides must be the same length in total as the one longer red side.
- The two green verticalGoing from up to down on this screen.sides must be the same length in total as the one longer red side.
- We can use this fact to find missing sides before we add them to find the perimeter.

- The missing verticalGoing from up to down on this screen.side plus 6 cm must equal 9 cm. The missing vertical side is 3 cm.
- The missing horizontalGoing from left to right across this screen.side plus 4 cm must equal 12 cm. The missing horizontal side is 8 cm.
- We find the perimeter by adding the outside edges of our shape.
- 8 cm + 12 cm = 20 cm and 4 cm + 6 cm = 10 cm. We can add these four sides to make 30 cm
- We add the remaining two sides to 30 cm. 30 cm + 9 cm = 39 cm and then 39 cm + 3 cm = 42 cm.
- The perimeter of this compound shape is 42 cm.

# Calculating the Perimeter of a Compound Shape made from Rectangles

**compound shape**(or composite shape) is a more complex shape that is

**made up of two or more simple shapes**.

We will be looking at compound shapes made specifically out of two combined rectangles.

We may be asked to find the perimeter of a compound shape like the one above.

For example:

To find the **perimeter**, we simply **add up the lengths of each outside edge**.

It may be helpful to look out for **number bonds** when adding the sides.

For example, 7 + 3 = 10.

The total of all of the outer sides is 36, so the **perimeter is 36 cm**.

In some perimeter questions, the lengths of **some of the sides may be missing**.

For example:

Two of the side lengths of this rectangular composite shape are **missing**.

We can use the other side lengths to work out what these missing values are.

Weâ€™ll begin with the missing

To find its value, we will look at the other vertical lengths.

Looking at the shape, the side that is **9 cm long** is the **same as** both the **missing side** plus the **side that is 6 cm long**.

9 cm = ? cm + 6 cm

We can therefore find the missing length by **subtracting** 6 cm from 9 cm.

9 â€“ 6 = 3

So, **the missing side length is 3 cm**.

Next, weâ€™ll find the missing

To find the missing horizontal length, we will look at the values of the other horizontal lengths.

Looking at the composite shape, **the side that is 12 cm long** is the **same as** both the **missing side** plus the **side that is 4 cm long**.

12 cm = 4 cm + ? cm

We can therefore find the missing length by **subtracting** 6 cm from 9 cm.

12 â€“ 4 = 8

So, the **missing length is 8 cm**.

Now that we know the lengths of all of the sides, we can find the perimeter of the composite shape.

Again, it may be helpful to look for **number bonds** to make the perimeter calculation easier.

For example, 12 + 8 = 20.

The total is 42, so the **perimeter of our composite shape is 42 cm**.

Now try our lesson on *Calculating Area of Rectangles and Squares* where we learn how to find the area of rectangles including squares.