The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

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: