Area of shaded region circle help 
Find the area of the shaded region


Area of the sector is $240^\circ$ or $\frac{4\pi}{3}$ 
Next find $\frac{b\cdot h}{2}$ which is $\frac{2\cdot2}{2}$ which is $2$.
Then subtract the former from the latter: $\frac{4\pi}{3} - 2$
Therefore the answer is $~2.189$?
Is this correct?

No, the  area that  corresponds to 120 degrees  or $\frac{2\pi}{3}$ is one third of the total area of the circle $4\pi$ the area of the triangle is $\frac{bh}{2}$ but $h$ is not $2$ you need to project it,  since $\cos (\, 30 \text{ degrees}) = \frac{\sqrt{3}}{2}$ degrees to find $h = \sqrt{3}$ Therefore 
$$\text{area} = \frac{4\pi}{3} - \sqrt{3}  = 2.4567 \cdots  $$

