Chapter 11.4, Problem 18PPS

To determine

To find: The area of each figure.

Answer to Problem 18PPS

The area of figure is $39.4{\text{mm}}^2$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

To find the area of the figure, add the area of the two rectangles and area of the quadrant circle.

Area of rectangle with dimension $3\text{mm}\times 3.5\text{mm}$ is calculated as:

  $\begin{array}{c}\text{Area}=\text{length×breadth}\\ =3.5\cdot 3\\ =10.5\end{array}$

Area of rectangle with dimension $3.5\text{mm}\times 5.5\text{mm}$ is calculated as:

  $\begin{array}{c}\text{Area}=\text{length×breadth}\\ =3.5\text{×}5.5\\ \approx 19.25\end{array}$

Area of the quadrant circle is calculated as:

  $\begin{array}{c}\text{Area}=\frac{1}{4}\left(\pi r^2\right)\\ \approx \frac{1}{4}\left(3.14{\left(3.5\right)}^2\right)\\ \approx 9.6\end{array}$

The area of shaded region is calculated as:

  $\begin{array}{c}\text{Area of figure}=\text{Area of two rectangle+}\left(\text{Area of quadrant circle}\right)\\ \approx 10.5+19.25+9.6\\ \approx 39.4\end{array}$

Therefore the area of figure is $39.4{\text{mm}}^2$ .