Problem:
What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale.)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Divide the square into smaller squares as shown. The shaded square is formed from halfsquares, so its area is . The ratio to is .
Note: There are several other ways to divide the region to show this.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions