Problem:
A park is in the shape of a regular hexagon km on a side. Starting at a corner, Alice walks along the perimeter of the park for a distance of km. How many kilometers is she from her starting point?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Consider the figure. We may assume that Alice starts at and ends at . Observe that in is right and has length . The Pythagorean Theorem shows that .
Consider the second figure. Observe that in
,
,
.
By the Law of Cosines,
Therefore .