Answer
$4\ inch^2$
Work Step by Step
Given
Length of the arc (L) = 4 inches
given the angle $(\theta)$= 2 radians
formula for the length of the arc is $L=r\theta$
$4 = r (2)$
$r=\frac{4}{2}= 2\ inches$
Area of the sector is $A =\frac{1}{2}r^{2}\theta$
$A=\frac{1}{2}(2)^2(2)$
$A=4\ inch^2$