Problem:
In convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles, and ∠B,∠C,∠E, and ∠F are congruent. The area of the hexagonal region is 2116(2​+1). Find AB.
Solution:
Because ∠B,∠C,∠E, and ∠F are congruent, the degree-measure of each of them is 4720−2⋅90​=135. Lines BF and CE divide the hexagonal region into two right triangles and a rectangle. Let AB=x. Then BF=x2​. Thus
