Solution: AE⊥BC,AF⊥CD, ∠ EAF = 45 ∴∠ AEC = ∞△ AFD = 90 in the quadrilateral AECF and ∵∴∠∠∠∠∠∠∠∠∠.

Let AE length be a, then AF=2, root number 2-a, then AB= root number 2a AD=4- root number 2a.

Quadrilateral perimeter =2AB+2AD=2 radical 2a+8-2 radical 2a=8.