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

$\frac{1}{2}(9\sqrt{3}-\frac{11}{7})$ unit²

Area of the shaded part = \(\frac{1}{2}\) x area of a triangle - Area of the sector

⇒ \(\frac{1}{2}\) x \(\frac{√3\; × \; 36}{4}\) - (\(\Pi \) x \( { r}^{2 } \) x \({90}^\circ\))/\({360}^\circ\)

⇒ (\(\frac{1}{2}\) x 9√3) - (\(\frac{22}{7}\)) x 1 x \(\frac{1}{4}\)

⇒ (\(\frac{1}{2}\) x 9√3) - (\(\frac{11}{7}\)) x 1 x (\(\frac{1}{2}\))

⇒ \(\frac{1}{2}\)(9√3 - \(\frac{11}{7}\))

Therefore, the answer is \(\frac{1}{2}\)(9√3 - \(\frac{11}{7}\)) unit² .