Chapter 11.6, Problem 5CE

To determine

To Find: The area bounded by $\overline{AB}and\stackrel{⌢}{AB}$

Answer to Problem 5CE

  $A=6\pi -9\sqrt{3}$

Explanation of Solution

Given: Radius = $6$ and $\stackrel{⌢}{mAB}=60$ .

Given: radius = $6$

  

We have to find the area of shaded region.

i.e.

Area of shaded region = area of sector − area of triangle

  $\begin{array}{l}=\frac{60}{360}\pi r^2\\ $ =\frac{1}{6}\pi {(6)}^2$=6\pi \end{array}$

Area of triangle

  $\begin{array}{l}$ A=\frac{\sqrt{3}}{4}{(side)}^2$$ A=\frac{\sqrt{3}}{4}{(6)}^2$A=\frac{36\sqrt{3}}{4}\\ A=9\sqrt{3}\end{array}$

Area of the shaded sector.

  $A=6\pi -9\sqrt{3}$