Since this is a circle question, you know the key is the radius. Since the test writer gave you the diameter of 8, you know the radius is 4, so the area of the circle is
. The area that interests you is defined by a right angle so that is 1/4 of the total area or
. When you subtract the area of the triangle (
) that leaves the shaded region.
Many students get as far as
but don't see their answer. In this case, they may recognize it as C but on the test the reduced answer may not be as obvious. Be sure to remember to reduce your answer whenever you can. It is a real shame to get the right answer but not get credit due to the failure to reduce.