Answer
$4\pi$ square in.
Work Step by Step
The formula $A=0.5r^2\theta$ requires the angles to be in radius. $\theta$ is currently in degrees, so we need to multiply it by $\pi/180$ to obtain it in radius.
Hence here the area of the sector: $A=0.5r^2\theta=0.5\cdot4^2(90)\pi/180=4\pi$ square in.