Problem:
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. 61​π−43​​
B. 43​​−121​π
C. 43​​−241​π
D. 43​​+241​π
E. 43​​+121​π
Solution:
First note that the area of the region determined by the triangle topped by the semicircle of diameter 1 is
