Chapter 7, Problem 2STP

To determine

To Find:

The equation that can be used to determine the total area of the given composite figure.

Answer to Problem 2STP

J

Explanation of Solution

Given Information:

Given figure is :

  

Formula Used:

Area of a rectangle having length l and width w is = lw

Area of a semi-circle having radius r is = $\frac{1}{2}\pi r^2$

Calculation:

  $\begin{array}{l}\text{The given figure is a composition:}\\ \text{1}\text{.}\\ \text{Rectangle of length 'l' and width 'w'}\\ \text{2}\text{.}\\ \text{Semi-circle of diameter = }l\\ \Rightarrow \text{radius r = }\frac{l}{2}\\ So,\text{ the area of the figure will be sum of areas of }\\ \text{the rectangle and the semi-circle}\text{.}\\ {\text{Area of the rectangle = A}}_1=lw\\ {\text{Area of the semi circle = A}}_2=\frac{1}{2}\pi r^2=\frac{1}{2}\pi {\left(\frac{l}{2}\right)}^2\\ Area{\text{ of the composite figure = A = A}}_1+A_2=lw+\frac{1}{2}\pi {\left(\frac{1}{2}l\right)}^2\\ Hence,\text{ J is the correct option}\text{.}\end{array}$