Chapter 12.2, Problem 40SR

To determine

The area of the figure:

  

Answer to Problem 40SR

The area of the figure is $12.878y{d}^2$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}l=3.5yd\\ w=d=2.8yd\end{array}$

Concept Used:

The area of the rectangle is given by the following expression:

  $A=l\times w$

Where,

Length of rectangle: $l$

Width of rectangle: $w$

The area of semi-circle is given by the following expression:

  $A=\pi \frac{r^2}{2}$

Where,

Radius of semi-circle: $r$

Calculation:

The area of the rectangle is given by the following expression:

  $A_1=l\times w$

Put the given values:

  $\begin{array}{l}{A}_1=l\times w\\ A_1=3.5\times 2.8\\ A_1=9.8y{d}^2\end{array}$

The area of the semi-circle is given by the following expression:

  $A_2=\pi \frac{r^2}{2}$

Put the given values:

  $\begin{array}{l}{A}_2=\pi \frac{r^2}{2}\\ A_2=\pi \frac{{\left(\raisebox{1ex}{$d$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2}{2}\\ A_2=\pi \frac{{\left(\raisebox{1ex}{$2.8$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2}{2}\\ A_2=\pi \frac{1.96}{2}\\ A_2=3.078y{d}^2\end{array}$

So, the total area of the figure:

  $\begin{array}{l}A=A_1+A_2\\ A=9.8y{d}^2+3.078y{d}^2\\ A=12.878y{d}^2\end{array}$

Conclusion:

Hence, the total area of figure is $12.878y{d}^2$