Because AB is parallel to DC in trapezoidal ABCD.

So BD can be translated into AE, and CD and E can be crossed to get parallelogram ABDE.

If a is the height of the CD edge and the vertical foot is F, then the meaning of the problem is AE=CH= 12.

In Rt△AFC, Pythagorean theorem is: CF = √ (AC 2-AF 2) = 12.

In Rt△AFE, Pythagorean theorem is: ef = √ (AE 2-AF 2) = 9.

Therefore: CE=CF+EF=25.

△ABC and△ △ABD are triangles with the same base and height because of CE‖AB.

So S△ABC=S△ABD

Because the parallelogram Abd, S△ABD=S△AED.

Therefore, S- trapezoid ABCD = s △ ABC+s △ ADC = s △ ADC+s △ ABC = s △ ace.

It is also known that in S△ACE, the base height AF= 12 and CE=25.

Therefore, S- trapezoid ABCD=S△ACE=AF×CE/2= 150.