Four, as shown in the figure, $P$ is a point inside the square $ABCD$, $PA=5$, $PB=8$, $PC=13$. Find the area of square $ABCD$.

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Four, Hint: Like tears, draw $P E \perp$ $A B, P F \perp B C$, and let the side length of the square be a, $\quad P_{E}=x, \quad P F$ $=y$, solve to get the area of square $A B C D$ is approximately 153.