Answer
$A(0)=796~cm^2$
If you want the maximum area, use all the wire to form the circle.
Work Step by Step
$A=\frac{(4+\pi)x^2-800x+40000}{16\pi}$
The parabola opens upwards. The maximum area must be one of the extremes. The vertex would give us the minimum area.
$A(0)=\frac{40000}{16\pi}=\frac{2500}{\pi}\approx796~cm^2$
$A(100)=\frac{(4+\pi)10000-80000+40000}{16\pi}=\frac{(4+\pi)625-2500}{\pi}=625~cm^2$
