You start by systematically naming each relevant unknown with a distinct letter.
[MATH]x = \text {length of lines AD and BC;}\\
y = \text {length of lines AB and CD;} \\
z = \text {area of rectangle ABCD;}\\
p = \text {length of line AE;}\\
q =\text {length of line BE; and}\\
r = \text {height of triangle BEF.}[/MATH]There may be other lengths or areas that will become relevant, but we have a start. That is six relevant unknowns so far. Thus, we need six independent equations Involving those unknowns.
Some are obvious.
[MATH]xy = z,\\
p + q = y,\\
\dfrac{1}{2} * px = 50, \text { and}\\
\dfrac{1}{2} * fq = 40.[/MATH]That means we must find at least two more equations (two if we discover no other relevant unknowns).
This has been relatively mechanical, naming things and looking for obvious relationships, but now we must begin to think. I can see immediately two ideas that may or may not be helpful.
I see two similar triangles, one with a known area. I don’t see an immediately obvious way that helps, but I haven't really thought about it . I know I can decompose this figure into five triangles, two with known areas. Again, the only way to know whether that helps or not is to think about it. How do we think about such amorphous things? We try them and see where they lead.