In the figure, ABC is an equilateral triangle with AB = 6. Find the area of the circumcircle.
We can find the radius of the circumcircle with the Law of Cosines
AB^2 = 2R^2 - 2R^2 cos (2 * angle BAC)
6^2 = 2R^2 - 2R^2 cos (120°)
36 = 2R^2 + R^2
36 = 3R^2
R^2 = 12
So....the area of the circumcircle = pi * R^2 = pi * 12 = 12 pi units^2
