Chapter 11.6, Problem 7PSA

To determine

To calculate: The area of the region.

Answer to Problem 7PSA

The area of the region is $228.53unit{s}^2$ .

Explanation of Solution

Given:

Side $AB=CD=10,$

Side $AD=BC=15.$

Formula Used:

Area of rectangle $=b\ast h$

b = Base,

h = Height.

Area of circle $=\pi r^2$

r = radius of a circle.

Calculation:

  

  $A(\square ABCD)=BC*DC=15*10=150unit{s}^2$

In above region, half of a circle lies left of AB and another half lies right of DC . These two areas of half circles represent area of one circle with diameter 10 units.

  $\begin{array}{l}d=AB=10\\ r=\frac{d}{2}=\frac{10}{2}=5\end{array}$

Area of circle $=\pi r^2$

  $\begin{array}{l}$ =\pi {(5)}^2$=25\pi \\ =78.53unit{s}^2\end{array}$

Area of region = Area of rectangle+ Area of circle

  $\begin{array}{l}=117-30-30-24\\ =150+78.53\\ =228.53unit{s}^2\end{array}$