ANSWER
The area of the shaded sector is
[tex]Area =\pi \: {in}^{2} [/tex]
EXPLANATION
The area of a sector is calculated using the formula,
[tex]Area = \frac{central \: angle}{360 \degree} \: \times \pi \: {r}^{2} [/tex]
Fro the diagram, the central angle is 90°
The radius of the circle is 2 in.
[tex]Area = \frac{90 \degree}{360 \degree} \: \times \pi \: {2}^{2} {in}^{2} [/tex]
[tex]Area = \frac{1}{4} \: \times \pi \: 4 {in}^{2} [/tex]
This finally simplifies to
[tex]Area =\pi \: {in}^{2} [/tex]
