Ok, here's my shot at this:

First you have done well so far, except that the formula will give you:

A = {(Pi)(r)^2}/4 + 2(r)(H) ... instead of : A = {(Pi)(r)^2}/4 + 2(Pi)(H)

Now, use the fact that:

Perimeter = pi*r + 4r + 2H , solve for H:

H = [P - pi*r - 4r]/2 ; where P is the Perimeter, which you were told it fixed; thus being a constant and (P)' = 0

Now you can follow the usual optimization process.