Please submit your concern

Explanation:

Let the length of each side of the hexagon be y.

Area of the hexagon = $\frac{3\sqrt{3}}{2}$y²

Area of the triangle = $\frac{\sqrt{3}}{16}$y²

Area of the shaded region = $\frac{23\sqrt{3}}{16}$ y² = X

y² = $\frac{16}{23\sqrt{3}}$X

Area of the circle = πy²

Thus, area of the circle in terms of X

= $\frac{16\pi }{23\sqrt{3}}$X

Hence, option (a).