Find area of shaded region in circle

Question

I am working on this SAT question.

Progress

• AD = 3

• largest radius =3

• second largest = 2

Answer 1

Since $AB=BC=CD=1$ $\implies$ $AE=6$$\hspace{0.2cm}$ and $\hspace{0.2cm}$$DE=3$$\hspace{0.2cm}$ because$\hspace{0.2cm}$$ D$ $\hspace{0.2cm}$is the center of largest circle.

Area of circle with diameter $CE=4$$\hspace{0.2cm}$ is $\hspace{0.2cm}$$\pi r^2=\pi 2^2=4\pi$

Area of circle with diameter $BE=5$$\hspace{0.2cm}$ is $\hspace{0.2cm}$$\pi r^2=\pi (\frac{5}{2})^2=\frac{25}{4}\pi$

Hence the area of shaded region$=\frac{25}{4}\pi-4\pi=\frac{9\pi}{4}$