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. 61βΟβ43ββ
B. 43βββ121βΟ
C. 43βββ241βΟ
D. 43ββ+241βΟ
E. 43ββ+121βΟ
Solution:
First note that the area of the region determined by the triangle topped by the semicircle of diameter 1 is
