TITLE: How to find the area of this square?
QUESTION [6 upvotes]: In a square $ABCD$, say there is a point $P$ which lies inside
  it, the point $P$ is located at distances $x$, $y$ and $z$ meters from
  $A,B$ and $C$ respectively.

Using this information how could we compute a form for the area of the square?Please explain your approach.

REPLY [2 votes]: This is just a supplement to Srivatsan's answer. I knew that this was a consequence of something but didn't quite get it but this is just Varignon's theorem. 

(I wish one day we can insert tikzpicture environment inside the answers.) I also agree with Srivatsan that there must a shorter/simpler observation and maybe someone can provide it.