AoPS Wiki:Problem of the Day/September 12, 2011

In trapezoid ABCD, AD ||BC. $\angle A = \angle D = 45\dgg$ (Error compiling LaTeX. Unknown error_msg), while $\angle B = \angle C =135\dgg$ (Error compiling LaTeX. Unknown error_msg). If AB=6 and the area of ABCD is 30, find BC.