Question

May someone please help me with this?

Answer 1

Answer:

Step-by-step explanation:

First, calculate the angle of FDE (assume it as α) by:

$EF=\frac{\alpha}{360}\times(2\pi)(DE) \rightarrow 2\pi = \frac{\alpha}{360}(2\pi)(6)$

$\alpha=60^{0}$

So, use this angle to calculate the area of FDE (unshaded region):

$A_{US}=\frac{\alpha}{360}\times(\pi)(DE)^{2}=\frac{60}{360}(\pi)(6^{2})=6\pi$

So, the shaded region can be determined by:

$A_{S}=A-A_{US}=\pi(DE)^{2}-6\pi=36\pi-6\pi=30\pi=\frac{60}{2}\pi$