Answer
$5.73\ ft^2$
Work Step by Step
Given
Length of the arc (L) = 3 feet
given the angle $(\theta)$= $\pi/4$
formula for the length of the arc is $L=r\theta$
$3 = r (\pi/4)$
$12=r\pi$
$r=\frac{12}{\pi}$
Area of the sector is $A =\frac{1}{2}r^{2}\theta$
$A=\frac{1}{2}(\frac{12}{\pi})^2(\frac{\pi}{4})$
$A=\frac{1}{2}(\frac{144}{\pi^2})(\frac{\pi}{4})$
$A= (\frac{144}{\pi^2})(\frac{\pi}{8})$
$A=\frac{18}{\pi}$
$A=\frac{18}{3.14}$ (since the value of $\pi$ is 3.14)
$A=5.73\ ft^2$
