Problem:
What is the area of the region in the coordinate plane defined by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Replacing by and by does not change the inequality, so the region is symmetric with respect to both coordinate axes. In the first quadrant the given inequality is equivalent to , and its graph is the square bounded by the lines , , and together with its interior. The area of this square is 2 . Therefore the area of the entire region is . (The region consists of the 4 shaded squares in the figure below.)
The problems on this page are the property of the MAA's American Mathematics Competitions