Cool Trapezoid Problem

So my friend from down the hall (and the one that got me started with bloging and twitter) took her GRE again yesterday.  I stopped by her room while passing by to see how it was and she said she had a problem SIMILAR to this and needed help with it.

I really like it!  I'm not sure if I worded it right but this is the jest that she was getting across to me when she was explaining the problem.
I was wondering if anyone had any other interesting brain teasers out there that wouldn't be totally beyond my students but that would make them think.  I really love problems like this and my kids tend to like them a lot too!