Geometry Problem: Find Overlapping Area

[preet]

I can't get this problem... no idea how to do it. Can't use coordinates / angles, just straightforward geometry. (by angles I mean, you can't use a calculator to find em, then do everything from there)

Any help appreciated... thanks

"A card 12cm long and 6 cm wide is cut along a diagonal to form two congruent triangles. The triangles are arranged as shown. Find the area of the region where the triangles overlap."

http://img314.imageshack.us/img314/7241/untitled8ew.gif

 

[Tide]

Draw a line segment from the right angle to the intersection of the two hypotenuses. You now have four small triangles. It should be evident (i.e. you should be able to prove) that all four triangles have the same area. It follows that the area of the overlap region is 2/3 the area of one of the original triangles.

 

[HallsofIvy]

Nice solution!