∵bd⊥dc,∴sin∠cbd=cd/bd,∴sin∠adb=cd/bc。

∴△ABD area = (1/2) ad× BDS in ∠ ADB = (1/2) ad× BD× CD/BC.

△ area of △BCD = (1/2) BD× CD.

∴ area of trapezoid ABCD = area △Abd+ area △ BCD = (1/2) BD× CD (ad/BC+1).

According to Pythagorean theorem, there are: BD 2+CD 2 = BC 2 = 16, while BD 2+CD 2 ≧ 2bd× CD, ∴BD×CD≦8.

∴ trapezoidal area ABCD ≦ (1/2) × 8 (ad/BC+1) = 4 (2/4+1) = 6.

That is, the maximum area of trapezoidal ABCD is 6.