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 \(AB\).

(第二十四届AIME2 2006 第1题)