In the figure above, AB is the diameter of a circle of radius 6, what is the perimeter of the shaded region?

$$A.\ \pi+6+6\sqrt{3}$$
$$B.\ \pi+12+6\sqrt{3}$$
$$C.\ 2\pi+9+6\sqrt{3}$$
$$D.\ 2\pi+12+6\sqrt{3}$$
$$E.\ 2\pi+12+12\sqrt{3}$$

The OA is D.

What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B.

Is there a strategic approach to solve this PS question? Can anyone help? Thanks!