Problem:
In rectangle ABCD,AB=6,AD=30, and G is the midpoint of AD. Segment AB is extended 2 units beyond B to point E, and F is the intersection of ED and BC. What is the area of BFDG?
Answer Choices:
A. 2133​
B. 67
C. 2135​
D. 68
E. 2137​
Solution:
Because △EBF is similar to △EAD, it follows that ADBF​=AEBE​, or 30BF​=82​, giving BF=215​. The area of trapezoid BFDG is
21​h(b1​+b2​)=21​⋅AB⋅(BF+GD)=21​⋅6⋅(215​+15)=(C)2135​​.
The problems on this page are the property of the MAA's American Mathematics Competitions
