The first problem is really hard if that's all there is to it. ABCD is any quadrilateral? No parallel sides? No given interior angle? Hard.
Just trying to figure how to get the area, S, of ABCD is very hard already.
In the second problem, you are on the right track. Continue with your computations and you should arrive to the conclusion that CH/AH = 21/11 indeed.
That is, (2a-b)/b = 21/11 according to your assumptions.