Answer
$\frac{29\pi}{2}$ square ft
Work Step by Step
Given-
Central angle of the sector. $\theta$ = $145^{\circ}$
or, $\theta$ = $145\times\frac{\pi}{180}$ = $\frac{29\pi}{36}$ rad
radius, r = 6 ft
A = ?
We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by-
A = $\frac{1}{2} r^{2} \theta$
= $\frac{1}{2}\times 6^{2}\times \frac{29\pi}{36}$
= $\frac{29\pi}{2}$ square ft