is the center of the circle and .

Area of the triangle is .

Observe the figure,

and are the radii of the circle.

Therefore, .

radius is he side of the equilateral triangle.

Thus the triangle is equilateral.

Assume .

Area of the equilateral triangle is .

.

Observe the figure,

Area of the shaded region is area of the sector minus  area of the triangle.

Area of the sector is .

Radius of the circle is .

Since the triangle is equilateral, then .

Area of the shaded region:

.

Option D is correct.

Option D is correct.