Question

Find the area of the shaded figure below round your answer to one decimal place

Answer 1

This is a complex figure, you have to calculate the area of the shaded figure.

If you look at the figure, you have to decompose it into simpler geometrical shapes first

The shape is composed of a rectangle and a semicircle. To calculate the shaded area, you have to calculate the area of the rectangle and the area of the semicircle. Then you have to subtract the area of the semicircle from the area of the rectangle to determina the area of the shaded portion.

`A_T=A_R-A_C`

"T" represents the shaded portion

"C" represents the semicircle

"R" represents the rectangle

First calculate the area of the rectangle

`\begin{gathered} A_R=w\cdot l \\ A_R=8\cdot18 \\ A_R=144 \end{gathered}`

Next calculate the area of the semicircle, to do so you have to calculate the area of the circle and divide it by 2

`\begin{gathered} A_C=(\pi r^2)/(2) \\ A_C=(\pi4^2)/(2) \\ A_C=8\pi \end{gathered}`

The area of the shaded part is

`\begin{gathered} A_T=A_R-A_C_{} \\ A_T=144-8\pi_{} \\ A_T=118.867\cong118.9 \end{gathered}`

The area of the shaded portion is 118.9