Problem:
Rectangle DEFA below is a 3×4 rectangle with DC=CB=BA=1. The area of the "bat wings" (the shaded area) is
Answer Choices:
A. 2
B. 221
C. 3
D. 321
E. 4
Solution:
The area of △BCE is 21(1)(4)=2. Triangles △CBH and △EFH are similar. Since CB=31EF, it follows that IH=31GH=41IG=1. The area of △CBH is 21, so the area of △ECH is 2−21=23. Thus the batwing's area is 3.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions
