In the diagram, line segment PS has length 4. Points Q and R are on line segment PS. Four semi-circles are drawn on the same side of PS. The diameters of these semi-circles are PS,PQ,QR, and RS. The region inside the largest semi- circle and outside the three smaller semi-circles is shaded. What is the area of a square whose perimeter equals the perimeter of the shaded region?
Answer Choices
A. 4
B. \pi
C. \pi^2
D. 2\pi^2
E. \frac{\pi^2}{4}