Chapter 11.4, Problem 17PPS

To determine

To find: The area of each figure.

Answer to Problem 17PPS

The area of figure is $55.6{\text{in}}^2$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

To find the area of the figure, add the area of the trapezium and area of three semi-circle.

The height of the isosceles triangle is calculated by using the diagram is as:

  $\begin{array}{c}h=\left(16-10\right)\text{cm}\\ =6\text{cm}\end{array}$

The area of shaded region is calculated as:

  $\begin{array}{c}\text{Area of figure}=\text{Area of trapezium+3}\left(\text{Area of semi circle}\right)\\ =\frac{1}{2}\left(\text{sum of the length of parallel sides}\right)\text{×}\left(\text{distance between the parallel sides}\right)+3\left(\frac{\pi r^2}{2}\right)\\ =\frac{1}{2}\left(6+9\right)\text{×}6+3\left(\frac{\pi {\left(1.5\right)}^2}{2}\right)\\ =55.6\end{array}$ .

Therefore the area of figure is $55.6{\text{in}}^2$ .