4.5 G) Area of Compound Shapes
- One method is to make the shape larger than it actually is and then take off the area that is missing.
- The other method is to split the shape into many smaller shapes and add the areas of the smaller shapes together.
It does not matter what method you use. Certain method will work better for certain questions.
What is the area of the compound shape below? All of the angles are 90° (right- angles).
This first method is going to involve us working out the area of the whole rectangle. We will then take off the area of the smaller rectangle that is missing.
The equation for working out the area of a rectangle is given below:
The area of the rectangle is 154 cm2.
The next step is to work out the area of the rectangle that has been taken off the larger rectangle. The length of this rectangle is 3 and the width of this rectangle is 4.
Therefore, the area of the rectangle that has been taken off is 12 cm2.
The final step is to minus this area from the area of the larger rectangle.
The area of the shape is 142 cm2.
The other method that can be used to find the area of a compound shape is to split the shape into smaller shapes, work out the area of each of the smaller shapes and then add these areas together.
From the diagram below, we can see that I split the shape up into two 1 large rectangle and two smaller rectangles.
Let’s work out the area of the larger rectangle first (which is labelled as 1). We are given the width of the rectangle, which is 14 cm. The next step is to work out what the length of the rectangle is. In the original composite shape diagram, we are given what the length of the top of the shape is (11 cm). We are also given the part of the rectangle that has been taken off (3 cm). This means that the length of the rectangle 1 is 8 cm (11 – 3). We are now able to work out the area of this rectangle by multiplying the length (8) by the width (14). This tells us that the area of rectangle 1 is 112 cm2.
The next step is to work out the area of rectangle 2. Rectangle 2 has a length of 3 cm and a width of 6 cm. The area of this rectangle is 18 cm2.
We now work out the area of rectangle 3. This rectangle has a length of 3 and a width of 4. This means that the area of this rectangle is 12 cm2.
The final step is to add the three different areas together.
Therefore, the area of the composite shape is 142 cm2. This is exactly the same area as we found when we used the previous method.