Chapter 12.6, Problem 57SPR

To determine

Calculate the area of the shaded region.

Answer to Problem 57SPR

The area of the shaded region is $308.57$ .

Explanation of Solution

Given information:

It is given in the question that, the figure is

  

Formula used:

  $\begin{array}{l}Areaoftheshadedregion\\ =\left(areaofcirclehavingradius12\right)–\left(areaoftrianglehavingbase 24andheight12\right)\\ =\left(\pi r^2\right)-\left(\frac{1}{2}*b*h\right)\end{array}$

Calculation:

  $\begin{array}{l}Areaoftheshadedregion\\ =\left(areaofcirclehavingradius12\right)–\left(areaoftrianglehavingbase 24andheight12\right)\\ =\left(\pi r^2\right)-\left(\frac{1}{2}*b*h\right)\\ =\left(\frac{22}{7}*12*12\right)-\left(\frac{1}{2}*24*12\right)\\ =\left(\frac{3168}{7}\right)-\left(\frac{288}{2}\right)\\ =452.57-144\\ =308.57\end{array}$