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π/4 radians___________3 ft

2π radians__________ 24 ft

2π r = 24

r = 24/π ft

Area of circle = π x (24² / π²) ft²

Area of circle = 576 / π ft²

Area of circle = 183•3 ft²

Area of sector = 1/8 x 183•3 = 22•9 ft²

Let the radius of the sector be r ft, then

r(pi/4)=3

=>

r=12/pi.

The area of the sector is

A=0.5(r^2)(pi/4)

=>

A=0.5[(12/pi)^2](pi/4)

=>

A=18/pi~5.73 ft^2

s = arc length ... T = the angle theta .... r = radius

s = Tr

3 = (pi/4) r

r = 12/pi

A = r^2 T/2 = (12/pi)^2 (pi/8)

A = 18/pi sq feet

If you continued the arc to a full circle, it would be 8x3 = 24 feet in circumference. Because π/4 is 1/8 of 2π, a full circle. 

diameter is 24/π, radius is 12/π

area is πr² = π(144/π²) = 144/π

that is for the full circle. The sector is 1/8 of that, so

area of sector = (1/8)(144/π) = 18/π ft² = 5.7 ft²