GMAT Problem Solving Question 41: Circles, arcs, and area

 
Try the following GMAT Problem Solving question that tests your ability to find areas of intersections of circles.

Question 41:

Three semicircles of radius $1$ are constructed on diameter $\overline{AB}$ of a semicircle of radius $2$. The centers of the small semicircles divide $\overline{AB}$ into four line segments of equal length, as shown below. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?

1. $\quad \pi-\sqrt{3}$

2. $\quad \pi-\sqrt{2}$

3. $\quad \dfrac{\pi+\sqrt{2}}{2}$

4. $\quad \dfrac{\pi+\sqrt{3}}{2}$

5. $\quad \dfrac{7}{6}\pi \; – \; \dfrac{\sqrt{3}}{2}$