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Omni-MATH / A square in the xy-plane has area A, and three of its vertices have x-coordinates 2, 0, and 18 in some order. Find the sum of all possible values of A.

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problem

A square in the xyxy-plane has area AA, and three of its vertices have xx-coordinates 2, 0, and 18 in some order. Find the sum of all possible values of AA.
Plain-text mathematical notation (without MathML)
A square in the xy-plane has area A, and three of its vertices have x-coordinates 2, 0, and 18 in some order. Find the sum of all possible values of A.
Original LaTeX notation
A square in the $xy$-plane has area $A$, and three of its vertices have $x$-coordinates 2, 0, and 18 in some order. Find the sum of all possible values of $A$.

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