2006 AIME II Problem 1

In convex hexagon ABCDEF, all six sides are congruent, \angle A and \angle D are right angles, and \angle B, \angle C, \angle E, and \angle F are congruent. The area of the hexagonal region is 2116(\sqrt{2}+1). Find AB.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.