a=39

Below is the figure fully dimensioned.

Quite interestingly, in all cases the total of the three trapezoid perimeters will equal 5a+b. Since in this case the total was 198, and a=13b, this provides a useful shortcut to the fact that b=3 and therefore a=39 (although of course deriving this fact is more work in the short term).

Despite the fact that you don’t need to calculate the lengths of each of the trapezoids, there is only one figure which satisfies the conditions.