Answer
$2.46$
Work Step by Step
The area $A$ of a sector with central angle of $\theta$ radians is
$ A_{s}=\displaystyle \frac{1}{2}r^{2}\theta$.
The area of a triangle with sides of lengths $a$ and $b$ and with included angle $\theta$ is
$A_{t}=\displaystyle \frac{1}{2} ab \sin\theta$
To convert degrees to radians, multiply by $\pi/180$.
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The shaded area is obtained by subtracting the triangle area from the sector area.
$A=A_{s}-A_{t}$
$A=\displaystyle \frac{1}{2}\cdot 2^{2}\cdot\frac{120\pi}{180} - \frac{1}{2} 2\cdot 2\cdot\sin 120^{o}$
The reference angle for $120^{o}$,
(q.II, sine is positive) is $60^{o}$,
and $\displaystyle \sin 120^{o}=\sin 60^{o}=\frac{\sqrt{3}}{2}$
$ A= \displaystyle \frac{4\pi}{3}-\sqrt{3}\approx$2.45673939722$\approx 2.46$
