Area of Compound Shapes with Rectangles

Area of Compound Shapes with Rectangles

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finding the area of a composite rectangle

  • A compound shape is a more complicated shape made up of several simpler shapes.
  • This shape is made up of two rectangles.
  • To find the area of a compound shape, find the areas of the simpler shapes and add them together.
  • We first split this shape into 2 rectangles.
  • The area of a rectangle is base × height.
  • The leftmost rectangle area is 5 × 3 = 15 cm2.
  • The rightmost rectangle area is 2 × 6 = 12 cm2.
  • We add the two rectangle areas to find the total area.
  • 15 cm2 + 12 cm2 = 27 cm2.

Find the area of each rectangle by multiplying its base by its height.

Add the areas of the rectangles together to get the total area.

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Area of compound shapes example with rectangles

  • We split this composite shape into 2 rectangles.
  • The area of each rectangle is base × height.
  • The area of the left rectangle is 6 × 12 = 72 cm2.
  • We need to find the base of the rectangle on the right.
  • We can see that the horizontal distance of 6 plus the missing side must equal 14 cm.
  • 14 – 6 = 8 cm and so the base of the right rectangle is 8 cm.
  • The area of the rightmost rectangle is 8 × 8 = 64 cm2.
  • We add the areas of the two rectangles to find the total area.
  • 72 + 64 = 136 cm2.

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Area of Compound Shapes Worksheets and Answers

Area of Compound Rectangles

What is a Composite Shape?

A composite shape, or compound shape, is a more complex shape made from two or more basic shapes.

Composite shape questions seen in school are most often formed from a combination of rectangles, triangles and sometimes semi-circles.

In this lesson, we are looking specifically at compound shapes made entirely from rectangles.

This is an example of compound shape made only from rectangles.

example of a compound rectilinear shape

We can see in the image below that the composite shape can be made from 2 rectangles.

The shape could also be described as an L-shape. It looks like a backwards capital L.

Sometimes these shapes may be informally described as an L-shape and whilst it is not their proper name, it allows us to easily recognise this style of composite shape.

L-shaped composite shapes are made from two rectangles.

area of a compound shape split into two rectangles

A rectilinear shape is a shape in which all sides meet at right angles.

More simply, a rectilinear shape must be made only from rectangles.

Since this lesson is looking at compound shapes made from rectangles, all shapes that we are looking at will be examples of rectilinear shapes.

Finding the Area of Rectilinear Shapes

To find the area of a rectilinear shape:

  • Split the shape into separate, non-overlapping rectangles.
  • Find the area of each rectangle by multiplying its base by its height.
  • Add the areas of each rectangle together to find the total area.

An L-shape is a common rectilinear shape that we see.

Below is an example of an ‘L-shaped’ compound shape.

example of an L-shaped compound rectilinear shape

To find the area of the L-shape, split it into two rectangles.

The L-shapes can always be split into two rectangles where one rectangle makes the vertical line of the ‘L’ and the other rectangle makes the horizontal line of the ‘L’.

area of a compound shape split into two rectangles

The next step is to work out the area of each rectangle by multiplying their base by their height.

The left rectangle base is 5 cm and its height is 3 cm.

We multiply 3 cm by 5 cm.

3 × 5 = 15 and cm × cm = cm2. The units for area are cm 2.

Its area is 15 cm 2.

We now find the area of the right rectangle.

area of a composite shape split into two rectangles

The base is 2 cm and the height is 6 cm.

2 × 6 = 12 and so, the area of this rectangle is 12 cm2.

We finally add the two areas together to find the total area of the composite shape.

15 + 12 = 27 and so, the area of the compound shape is 27 cm2.

How to find the area of a compound shape example

Here is another compound L-shape example.

Before dividing the compound shape into two rectangles, we choose the rectangles so that we have the height and base of both.

example of finding the area of an l-shape

We divide the rectangle as shown.

The base of the bottom rectangle is 10 cm and the height is 6 cm.

Its area is 6 × 10 = 60 cm2.

The base of the top rectangle is 4 cm and its height is 5 cm.

Its area is 4 × 5 = 20 cm2.

We add the two areas together to find the area of the composite shape.

60 + 20 = 80 cm2.

Notice that we split the L-shape in this way so that the base and height of each rectangle were already labelled for us.

How to Find the Area of Compound Shapes with Missing Sides

We can find the area of compound shapes by finding the area of each of the basic shapes that make it and then adding them up.

Sometimes we need to work out the lengths of sides that have not been given to us. If a compound shape has missing sides, then the first thing to do is to work them out by comparing them to other sides of the shape.

Here is an example of a composite shape with missing side lengths.

We can see that we have sides of 6 cm, 12 cm, 14 cm and 8 cm but we do not have the two sides shown in the bottom right of the shape.

a composite shape with missing sides

We can split the shape into 2 rectangles.

The leftmost rectangle area is 6 × 12 = 72 cm2.

finding a missing side of a shape

However we can see that in the next rectangle, we do not have the length of the base side shown.

The height is 8 cm but we must work out the base.

how to find the length of a side of a shape

To find the missing side of a shape, compare its length to the length of a parallel side.

We can see in the image below that the red arrow and blue arrow shown must be as long as the top side.

The top side is 14 cm and the blue arrow is 6 cm.

area of a compound shape split into two rectangles

14 – 6 = 8 and so, the red arrow side must be 8 cm.

We can now work out the area of this rightmost rectangle by multiplying the base and the height.

8 × 8 = 64 and so the area of the rightmost rectangle is 64 cm2.

how to work out the area of a composite shape with steps shown

We finally add the areas of the two rectangles together.

We have 72 + 64.

70 + 60 = 130 and 2 + 4 = 6.

working out the area of a compound shape with missing sides.

72 + 64 = 136 and so the total area of this compound shape is 136 cm2

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Now try our lesson on What is the Volume of a Cuboid? where we learn how to find the volume of a cuboid.