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This problem trains for: SAT-I, AMC-8, GMAT.
In regular hexagon ABCDEF (convex polygon with six sides) with side length 2 we draw the diagonals AC, FD and BE. What is the area of the shaded region?
Denote the two points where the diagonals intersect by M and N.
The triangle AMB is 30° -60° -90°. Since the hypotenuse AB has length 2, then the leg AM which is opposite to the 60° angle has length:
and the area of FAMN is: