"How large is the room?" is wrong.
I think that should indeed be accepted. "What is the area..." is technically correct but sounds very technical. I would prefer "What is the size of that room?" or "How large is that room?"
It's not wrong -- it's just slightly different from the Indonesian sentence given. And with the Green Owl slightly different is not right.
the sentence is indeed very unnatural in English. You would say how "large is the room" or "what is the surface area of that room"