Answer:
Step-by-step explanation:
First, calculate the angle of FDE (assume it as α) by:
[tex]EF=\frac{\alpha}{360}\times(2\pi)(DE) \rightarrow 2\pi = \frac{\alpha}{360}(2\pi)(6)[/tex]
[tex]\alpha=60^{0}[/tex]
So, use this angle to calculate the area of FDE (unshaded region):
[tex]A_{US}=\frac{\alpha}{360}\times(\pi)(DE)^{2}=\frac{60}{360}(\pi)(6^{2})=6\pi[/tex]
So, the shaded region can be determined by:
[tex]A_{S}=A-A_{US}=\pi(DE)^{2}-6\pi=36\pi-6\pi=30\pi=\frac{60}{2}\pi[/tex]
