What is the area of trapezoid BEDC?

Whenever you have a geometry problem that asks you for dimensions of a figure that you cannot find, step back and find another way to look at it. Sometimes the best way to find the area of a particular figure is to think of negative space - subtract what you don't want from a larger figure.

You're right - there is no way to find the height of that trapezoid (at least no way that the GMAT would expect you to know). So you should ask yourself - why is that larger triangle there? Shapes within other shapes always exist to show us relationships.

Rahul is right - these are similar triangles. Whenever a line within a triangle is parallel to one of the sides, it creates two similar triangles. We can simply find the area of the large triangle, then subtract the area of the smaller one, and we'll be left with the area of the trapezoid, as in Rahul's explanation.

Another possibility (which we can't see without the answer explanations here) would be to estimate. If you're not told that the figure is NOT to scale, you know that it is roughly to scale, and you could possibly eyeball those measurements: "the height seems to be roughly 2..." etc.