Perimeter of Compound Shapes: Composite Rectangles

Perimeter of Compound Shapes: Composite Rectangles
summary

Perimeter Compound Shapes Summary

  • 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.

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Perimeter of a Compound Shape

  • 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.

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Perimeter of Compound Shapes Worksheets and Answers

Calculating the Perimeter of a Compound Shape made from Rectangles

A 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.

What is a compound shape made up of two rectangles?

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

For example: Finding the perimeter of a compound shape made of two rectangles

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.

Finding the perimeter of a compound shape made of two rectangles

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:

Finding missing side lengths of compound shapes

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.

Finding missing side lengths of compound shapes

We’ll begin with the missing

verticalGoing from up to down on this screen.
length.

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

Finding missing side lengths of compound shapes

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 – 6 = 3

So, the missing side length is 3 cm.

Finding missing side lengths of compound shapes

Next, we’ll find the missing

horizontalGoing from left to right across this screen.
length.

Finding missing side lengths of compound shapes

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

Finding missing side lengths of compound shapes

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 – 4 = 8

So, the missing length is 8 cm.

Finding missing side lengths of compound shapes

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.

Perimeter of a compound shape with a perimeter of 42cm

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

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