Problem:
In trapezoid ABCD,AD is perpendicular to DC, AD=AB=3, and DC=6. In addition, E is on DC, and BE is parallel to AD. Find the area of â–³BEC.
Answer Choices:
A. 3
B. 4.5
C. 6
D. 9
E. 18
Solution:
Note that ABED is a square with side 3. Subtract DE from DC, to find that EC, the base of △BEC, has length 3. The area of △BEC is 21​⋅3⋅3=29​=4.5.
OR
The area of the △BEC is the area of the trapezoid ABCD minus the area of the square ABED. The area of △BEC is 21​(3+6)3−32=13.5−9=4.5.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions
