A semicircle of diameter 1 sits at the top of a semicircle of diameter 2 , as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.
Answer Choices
A. \dfrac{1}{6} \pi-\dfrac{\sqrt{3}}{4}
B. \dfrac{\sqrt{3}}{4}-\dfrac{1}{12} \pi
C. \dfrac{\sqrt{3}}{4}-\dfrac{1}{24} \pi
D. \dfrac{\sqrt{3}}{4}+\dfrac{1}{24} \pi
E. \dfrac{\sqrt{3}}{4}+\dfrac{1}{12} \pi