Your painting is not very standard. Draw it again. Then make two high AE and AF of trapezoid.

It can be seen from the meaning of the question that △BDC is an isosceles right triangle BC = 8, and let DC (= BD) = X.

Then X=4 times the root number 2.

Height AF is not only the height of trapezoid, but also the height of △BDC. From the properties of isosceles right triangle, it can be concluded that △DFC is also an isosceles right triangle FC= half BC=4. If there is Pythagorean theorem, it can be concluded that DF=4.

Because FC=4 EF=AD= 1, so

In the right triangle AEB, be = 3ae = 4, so AB = 5.