The Phases of the Moon Can Be Described Using the Phase

The phases of the moon can be described using the phase angle $\theta$ , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, $\theta$ changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by $A = \frac { 1 } { 2 } \pi R ^ { 2 } ( 1 + \cos \theta )$ , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: $\theta = 84 ^ { \circ }$

A) A = 8,094,766 mi ²
B) A = 3,654,317 mi ²
C) A = 586,254 mi ²
D) A = 3,175,511 mi ²
E) A = 2,023,691 mi ²