Question 15A 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. $\dfrac{1}{6}\pi - \dfrac{\sqrt{3}}{4}$$\dfrac{\sqrt{3}}{4} - \dfrac{1}{12}\pi$$\dfrac{\sqrt{3}}{4} - \dfrac{1}{24}\pi$$\dfrac{\sqrt{3}}{4} + \dfrac{1}{24}\pi$$\dfrac{\sqrt{3}}{4} + \dfrac{1}{12}\pi$
