=(1/(pi))*( (64+16(pi) )/(16+8(pi)+(pi)^2))-32/(4+(pi))+4)
This number is about .560.
Thus, we see that the minimum area is attained when x, the side length of the square, is 4/(4+(pi)), meaning the total amount given to the square is 16/(4+(pi)). Similarly, we see that the maximum area is attained when x is 0, giving all the length of the wire to the circle. (This mkes sense since a circle is the geometric shape with the greatest area/perimeter ratio.) So, the answers to the two parts above are:
(a) Give all 4 feet of wire to the circle and none to the square.
(b) Give 16/(4+(pi)) feet of wire to the square and the rest to the circle.
Hope that helped.