A circle has a total measure of 360º. To find the area of the shaded sector, you must find the fraction of the circle that is shaded.
If the smaller angle of the non-shaded area is 90º, the shaded portion's angle must be 270º.
This portion represents the fraction of the area that the shaded sector represents in the circle.
The area of a circle is π(r2).
Substituting in 9 ft for the radius, we get about 254.4 ft2 for the total area of the circle.
See part (a).