Find the area of the shaded portion of an equilateral triangle with sides 6 units shown in the following figure. A circle of radius 1 unit is centred at midpoint of a side of the triangle.

A

$$\frac{1}{2}\left(9\sqrt{3} - \frac{11}{7}\right)$$ unit$$^2$$

B

$$\frac{1}{4}\left(9\sqrt{3} - \frac{11}{7}\right)$$ unit$$^2$$

C

$$\frac{1}{2}\left(6\sqrt{3} - \frac{11}{7}\right)$$ unit$$^2$$

D

$$\frac{1}{2}\left(9\sqrt{3} - \frac{22}{7}\right)$$ unit$$^2$$