In trapezoidal ABCD, ab ‖ CD, CE bisects ∠ BCD, and CE ⊥ ad is at point E, de = 2ae, the area of △ CDE is 8, then the area of trapezoidal ABCD is () A.16 B.15 C.14 D.13 The answer seems to be B, but please tell me why

In trapezoidal ABCD, ab ‖ CD, CE bisects ∠ BCD, and CE ⊥ ad is at point E, de = 2ae, the area of △ CDE is 8, then the area of trapezoidal ABCD is () A.16 B.15 C.14 D.13 The answer seems to be B, but please tell me why

Because CE bisects BCD and CE ⊥ DF, it is easy to prove that △ CEF is equal to △ CED, then s △ FCD = 2S △ CED = 16; de = EF and AB / / CD, then △ FBA ∽ fcdde = 2ae = EF, AF: FD = 1:4, then s △ Fab = (1 / 4) ^ 2 * s △ FCD = 1 / 16 * 16 = 1, so s trapezoid = s △ fcd-s △ Fab = 16-1