Answer
$A=\frac{x^2}{16}+\frac{10000-200x+x^2}{4\pi}=\frac{(4+\pi)x^2-800x+40000}{16\pi}$
Work Step by Step
The length of each side of the square: $\frac{x}{4}$
The area of the square: $A=(\frac{x}{4})^2=\frac{x^2}{16}$
The length of the wire used to form the circle: $100-x=2\pi r$
$r=\frac{100-x}{2\pi}$
The area of the circle: $A=\pi r^2=\pi(\frac{100-x}{2\pi})^2=\frac{(100-x)^2}{4\pi}=\frac{10000-200x+x^2}{4\pi}$
The combined area:
$A=\frac{x^2}{16}+\frac{10000-200x+x^2}{4\pi}=\frac{(4+\pi)x^2-800x+40000}{16\pi}$
