Chapter 12.5, Problem 37S

To determine

The area of the each figure:

  

Answer to Problem 37S

The area of the given figure is $1240.88m^2$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}d=w=25m\\ l=30m\end{array}$

Concept Used:

The area of semi-circleis given by the following expression:

  $A=\frac{\pi r^2}{2}$

Where,

Radius of semi-circle: $r$

The area of rectangle is given by the following expression:

  $A=wl$

Where,

Width of rectangle: $w$

Length of rectangle: $l$

Calculation:

From figure:

There are two semi circles of same size and one rectangle as:

  

The area of semi-circle1 is given by:

  $A=\frac{\pi r^2}{2}$

Put the given data:

  $\begin{array}{l}{A}_1=\frac{\pi r^2}{2}\\ A_1=\frac{\pi {\left(\raisebox{1ex}{$d$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2}{2}\\ A_1=\frac{\pi {\left(\raisebox{1ex}{$25$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2}{2}\\ A_1=245.44m^2\end{array}$

The area of semi-circle2is same as area of semi-circle1:

  $A_2=A_1=245.44m^2$

The area of rectangle is given by the following expression:

  $A_3=wl$

Put the given data:

  $A_3=wl=25\times 30=750m^2$

So, total area of figure is calculated as:

  $\begin{array}{l}A=A_1+A_2+A_3\\ A=245.44m^2+245.44m^2+750m^2\\ A=1240.88m^2\end{array}$

Conclusion:

Hence, the area of figureis $1240.88m^2$ .