Chapter 11.8, Problem 8ST2

To determine

To Find: The area of shaded region.

Answer to Problem 8ST2

  $36\pi -27\sqrt{3}sq.units$

Explanation of Solution

Given:

  

Area of circle.

  $\begin{array}{l}{A}_c=\pi r^2\\ $ A_c=\pi {(6)}^2$A_c=36\pi \end{array}$

Area of triangle.

  $\begin{array}{l}{A}_t=\frac{1}{2}ap\\ A_t=\frac{1}{2}\times 3\times 18\sqrt{3}\\ A_t=27\sqrt{3}\end{array}$

Area of shaded region.

  $\begin{array}{l}A=A_c-A_t\\ A=36\pi -27\sqrt{3}sq.units\end{array}$

Hence, area is $36\pi -27\sqrt{3}sq.units$ .