A plane contains points A and B with A B=1. Let S be the union of all disks of radius 1 in the plane that cover \overline{A B}. What is the area of S ?
Answer Choices
A. 2+\sqrt{3}
B. \dfrac{8}{3}
C. 3 \quad \dfrac{\sqrt{3}}{2}
D. \dfrac{10}{3} \quad \sqrt{3}
E. 4 \quad 2 \sqrt{3}