1. What are Compound Shapes?
A compound shape is made up of two or more basic shapes joined together. The basic shapes are squares, rectangles, triangles etc. The compound shape below is made up of a square and a triangle.
1.1 How to find the Area of Compound Shapes?
To find the area of compound shapes, divide the compound shape into smaller shapes, then find the area of each of the smaller shapes and add them. Our final answer must be in square units e.g. m², cm², in² or ft², etc.
For example,
The compound shape is made up of rectangle A and square B.
| Area of Compound Shape = Area of Rectangle A + Area of Square B |
1.2 How to find the Perimeter of Compound Shapes?
The perimeter of a shape is the total distance around its edge. To calculate the perimeter of a shape, you just have to add up the lengths of all of its sides. In Compound shapes, the lengths of some of the sides may be missing. To work out the missing lengths we can use the other side lengths. Let’s learn this with an example.
In the shape above to calculate the perimeter, we need to know the two missing lengths.
The vertical length will be 9 cm - 5 cm = 4 cm
The horizontal length will be 11 cm - 4 cm = 7 cm
We can find the perimeter by adding the length of every side of the figure together:
Perimeter = 9 + 4 + 4 + 7 + 5 + 11 = 40 cm
1.3 Examples on Compound Shapes
Example: Find the area and the perimeter of the compound shape below.
Solution: Let’s split the shape into two rectangles and find the missing lengths.
Perimeter = 4 + 6 + 6 + 3 + 10 + 9 = 38 cm
Area of rectangle = length × width
Area of rectangle A = 4 × 6 = 24 cm²
Area of rectangle B = 10 × 3 = 30 cm²
Area of compound shape = Area of rectangle A + Area of rectangle B
Area of compound shape = 24 + 30= 54 cm²
Example: Work out the area of the compound shape given below.
Solution: Let’s split the shape into a rectangle and a trapezium.
Area of rectangle A = length × width
= 10 × 6
= 60 in²
Area of trapezium B = 1⁄2 × (sum of parallel sides) × height
Height of trapezium = 12 - 6 = 6 in
Area of trapezium B = 1⁄2 × (8 + 10) × 6
= 18⁄2 × 6
= 9 × 6
= 54 in²
Area of compound shape = Area of rectangle A + Area of trapezium B
= 60 + 54
= 114 in²
