Let \(A = (0,0)\) and \(B = (b,2)\) be points on the coordinate plane. Let \(ABCDEF\) be a convex equilateral hexagon such that \(\angle FAB = 120^\circ,\) \(\overline{AB}\parallel \overline{DE},\) \(\overline{BC}\parallel \overline{EF,}\) \(\overline{CD}\parallel \overline{FA},\) and the y-coordinates of its vertices are distinct elements of the set \(\{0,2,4,6,8,10\}.\) The area of the hexagon can be written in the form \(m\sqrt {n},\) where \(m\) and \(n\) are positive integers and n is not divisible by the square of any prime. Find \(m + n.\)
(第二十一届AIME2 2003 第14题)