How to Find the Area of Composite Shapes?

The composite shape consists of the main shapes together. The area of the composite shape is found by adding all the basic shapes.

Step by step guide to finding the area of composite shapes

The area of the composite shapes is the area of combined shapes of one or more simple polygons and circles. To calculate the area of composite shapes, we can add the area of all the major shapes together. The following figure gives an idea of finding the area of a composite shape. The unit area of compound shapes is expressed in \(m^2\), \(cm^2\), \(in^2\) or \(ft^2\), and so on.

How to find the area of composite shapes?

The area of composite shapes is a combination of basic shapes. With the following steps, we can calculate the area of the composite shapes.

• Break the compound shape into basic shapes.
• Find the area of each original shape.
• Add all the areas of basic shapes together.
• Show the answer in square units.

To decompose a composite shape, we need to calculate the area of some major shapes such as squares, triangles, rectangles, and so on. Check the table below for the area of the main shapes.

Finding the Area of Composite Shapes – Example 1:

Find the area of this composite shape.

Solution:

The length and breadth of rectangle \(ABCD\) are \(2\space in\) and \(7\space in\).
The length of the side of the square \(DEFG\) is \(3\space in\).

Using the formula for the area of the composite shape,

Area of composite shape \(=\) Area of rectangle \(+\) area of the square \(=(\:Length\:×\:Breadth\:)+\:side^2\)
\(=(BC × AB) + DE^2\)
\(=(2 × 7) + 3^2\)
\(= 14+9 = 23 \space in^2\).

Exercises for Finding the Area of Composite Shapes

Find the area of each composite shape.

• A composite shape has an area of \(620 \space cm^2\). The shape consists of a circle and a triangle and the area of the triangle is \(450 \space cm^2\) square units. What is the area of the circle?

• \(\color{blue}{1,876}\)
• \(\color{blue}{54}\)
• \(\color{blue}{170 \space cm^2}\)