Area of Composite Figures

Concept

The area of composite shapes is the area that is covered by any composite shape. The composite shape is a shape in which few polygons are put together to form a required shape. These shapes or figures can be made up of a combination of triangles, squares, and quadrilaterals, etc. Divide a composite shape into basic shapes like square, triangle, rectangle, hexagon, etc. to determine the area of composite shapes.

Rules

1. Decompose the composite figure into simpler shapes of which you can find the area.
2. Write down the area formulas of the simpler shapes.
3. Substitute the given values into the formulas.
4. Add or subtract the areas of the simple shapes as needed and state the correct square units.

Example

Find the area of the figure below. Use 3.14 for π.

Solution

The figure is made up of a semicircle and a triangle.

Area of the figure = Area of semicircle + Area of triangle

$\fn_phv =\frac{1}{2}\pi r^{2}+\frac{1}{2}bh$

$\fn_phv =\frac{1}{2}(3.14) (3\;cm)^{2}+\frac{1}{2}(6\;cm)(7\;cm)$

$\fn_phv {\color{Red} = 35.1\;cm^{2}}$

Practice Area of Composite Figures

Practice Problem 1

Find the area of the figure below.

Practice Problem 2

Find the area of the shaded figure below. Round your answer to the nearest tenth.

Practice Problem 3

Find the area of the shaded figure below. Use 3.14 or $\fn_phv {\color{Teal} \frac{22}{7}}$ for π, as needed. Round your answer to the nearest tenth.