Let each side of hexagon be 6
Here, AEC is an equilateral triangle with each side \(6\sqrt{3}\)

Area of shaded region = Area of hexagon - Area of equilateral triangle
= \(6\frac{\sqrt{3}}{4}6^2 - \frac{\sqrt{3}}{4}(6\sqrt{3})^2\)

= \(3(\frac{\sqrt{3}}{4}6^2)\)

Now, what percent of the area of the circle shown is shaded = \(\frac{Ar. of shaded region}{Ar. of circle}\)
= \(\frac{3\sqrt{3}}{4π} = 41.34\)%

Hence, option D

Key points:
1. AEC is an equilateral triangle
2. Radius of circle is equal to the side of regular hexagon
3. A hexagon's area equals the area of 6 equilateral triangles with same side length