MathDB

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.

Problem Statement