If you read the first post, I do state it's a parallelogram by stating AD || BC and AB || DC.
The last version of the pic., again, does not give sufficient info:
you can change the angle BAD, and obtain different values of parallelogram’s area.
The fact that in your picture B is strictly above D does not help: it could be merely a coincidence. So in the end the picture doesn’t let us to correctly infer that ABD is right triangle. On real GMAT pictures, all measures that intended to be fixed, are explicitly fixed.
So I think this would be somewhat more proper picture:
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Also, you need to state that ABCD is parallelogram.