Answer
$1.047 \text{ in}^2$
Work Step by Step
$\because A = \dfrac{1}{2}r^2 \theta$
where
$r$: Radius of the circle
$\theta$: Central angle that subtends the arc (in radians)
$A$: Area of the sector of the circle formed by the central angle $\theta$
Converting $\theta$ from degrees to radians:
$$\theta = 30 \times \dfrac{\pi}{180}= \dfrac{\pi}{6} \text{ radians}$$
Using the formula above gives:
$A= \dfrac{1}{2}\times (2)^2 \times \dfrac{\pi}{6} \approx \boxed{1.047 \text{ in}^2}$
