Area of a window problem

Help me /b/.
If the perimeter of this window is 20 feet, for what value X will the area be the greatest? I worked for about an hour on this and a similar problem, and I kept getting incorrect answers. UGH! The perimiter of the top portion is pi*x and the area of it is 1/2*pi*x^2. Can anyone give me any hints? I tried assigning the variable y to the two sides, and set up an equation for the perimeter as x + pi*x + 2y = 20, then solved for y. I then stuck that in the equation x*y + 1/2*pi*x^2 = A but for the maximum A I kept getting negative numbers. WHAT TO DO?!?!

Please see http://img247.imageshack.us/img247/2791/normanwindowwt8.jpg for a poorly drawn diagram.

x + pi*x + 2y = 20
x(1 + pi) + 2y = 20
y = 10 - x(1+pi)/2

A = xy + (pi*x^2)/2
A = x(10 - x(1+pi)/2) + (pi*x^2)/2
A = 10x - (1+pi)(x^2)/2 + pi(x^2)/2
A = 10x - ((x^2)/2)(1 + 2pi)
dA/dx = 10 - (1+2pi)x
dA/dx = 0 when
x = 10/(1+2pi)