$Required\,Area\,=\,Area\left \{ Sector(OBC)\,+\,Triangle(OBE)\right \}$
$Area\,of\,sector\,=\,\frac{1}{2}\times r^{2}\times\theta\,(\,\theta\, is\, in\, Radian)$
In, $\bigtriangleup OAB,\,sin(y) = \frac{AB}{OB} = \frac{1}{2}, (y) = sin^{-1}(\frac{1}{2}), (y)=30^{\circ}$
$(y) = 30\times (\frac{\pi}{180}) = \frac{\pi}{6}$ (Radian)
$Area\,of\,sector\,(OABC)=\,\frac{1}{2}\times r^{2}\times(y)=\,\frac{1}{2}\times 2^{2}\times(\frac{\pi}{6})=\,\frac{\pi}{3}$
$BE =\sqrt{OB^{2} - OE^{2}} = \sqrt{2^{2}-1^{2}} = \sqrt{3}$
$Area\,of\,\bigtriangleup OBE = \frac{1}{2}\times BE\,\times OE = \frac{\sqrt{3}}{2}$
$Required\,Area = \frac{\pi}{3} + \frac{\sqrt{3}}{2}$