Geometry

First, let's note that the median of the trapezoid is half the sum of the two bases. 

The area is irrelevant to the problem.

If one of the bases has length $12$, then the other base must have length $12+16=28$

Thus, the median is $\frac{28+12}{2} = 40/2 = 20$

So 20 is our ansswer. 

Thanks! :)