The diameter of AB=2BC = 2 * 2 = 4. What you will need to do is find the area of the biggest circle (with diameter AC), divide it by 2, then subtract half the area of the circle with diameter AB add half the area of circle BC.
First, the area of the big circle:
d=4 + 2 = 6
area=P d
6P = area of circle AC
Divide by 2:
6P / 2 = 3 P
Subtract half the area of circle AB:
Area AB/2 = P d /2
d = 4
area AB/2 = 4 P/2 = 2
3P - 2P
=P
Add half the area of circle BC:
AreaBC= 2P
2P + P
= 3P (D).
If pressed for time, since this is the last problem, you could also estimate the answer. You can see the diameter AC is 6 so the radius would be 3, giving the biggest circle an area of 9P. Half of that would be 9/2. Looking at the figure shows that the shades region will be slightly less than half of the circle, so you cab\n estimate and come up with D