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AB is the length of the side of the parallelogram, which is obviously not perpendicular to BE, so we can't use it for area calculations.

I did my calculations based on the diagram you drew. I didn't need to assume that the height of ABE and the height of ABCD are the same - the diagram shows that they ARE the same.

Draw a line perpendicular to BC that touches the line AD. The length of that new line is "h"

I fully understand it now. Thank you sooooo much!!!!!!!!!!!!