a. A sector that has been cut out of circular plastic sheet which has a circumference of 12.31 m. If the central angle of the sector is 1/4 of a revolution, find the area of the sector.

Answer 1

This is not trig.
Anyway, C=2(pi)r. If the circumference is 12.31, then the radius is 12.31/[(pi)r] = 1.96. If the central angle is 1/4 of a revolution, then the central angle measure is 90 degrees.
The area of a sector is a piece of the area of the entire circle:
A=(pi)r^2 * central angle measure/360
A=(pi)1.96^2 * 90/360
A=3 m^2