Area of Compound Figures

A compound figure is made up of two or more simple figures. The following figure is made up of a rectangle and a square. If we want to find the perimeter and area of a compound figure, then calculate the area of each simple figure and then find the sum of the area calculations.


Examples to Find the Area of Compound Figures:


Example 1: Find the area of the following compound figure.

Solution: Area of Rectangle Formula = l × b square units.

where, l is length,

b is breadth.

Rectangle 1 => 8 × 3 square units.

=> 24 square units.

Rectangle 2 => 6 × 3 square units.

=> 18 square units.

Rectangle 3 => 6 × 3 square units.

=> 18 square units.

Therefore the total area of compound figure = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3.

=> 24 + 18 + 18 square units.

=> 60 square units.

Hence the total area of compound figure is 60 square units.


Example 2: Find the area of the shaded part of the compound figure.

Solution: Area of Square = a2 square units.

where, a is length of the side of the square.

=> Area of Square = 82 square units.

=> 64 square units.

Area of Circle = ? r2 square units.

where, r is the radius of the circle.

=> Area of Circle = ? × 32 square units.

=> 3.14 × 9 square units.

=> 28.25 square units.

Therefore the area of the shaded part of the compound figure = Area of Square ? Area of Circle.

=> 64 ? 28.25 square units.

=> 35.75 square units.

Hence the area of the shaded part of the compound figure is 35.75 square units.


Practice Problems for Finding the Area of Compound Figures:


Questions: Find the area of the following compound figures.

Solutions: Compound Figure 1 = 28 square units.

Compound Figure 2 = 56 square units.