Hi @ippo232. It is a nice problem.
The problem is the same, no matter which reference place we choose. So, we can think about these three circles.
The circumference in black has equation
the circunference in red has equation
and the circunference in green has equation
The shaded areas are equal in size, that is, just calculate the area of one and multiply it by three.
So making use of
we have that the shaded area is
.
I repeat, it is a nice problem.
Greetings from Venezuela
The shaded area will form a semi circle.
1/2 X pi X 2 X 2 = 2pi
Answer is 2pi