### Instruction: A regular hexagon is inscribed in a circle of radius 2 units. In square units, what is the area of the hexagon? Express your answer in simplest radical form.### Response: A regular hexagon has six equal sides and six equal angles of 120 degrees each.
To find the area of the hexagon, I can divide it into six congruent equilateral triangles, each with a side length equal to the radius of the circle, which is 2 units.
The area of one equilateral triangle is given by the formula A = sqrt(3)/4 * s^2, where s is the side length.
So the area of one equilateral triangle in this hexagon is A = sqrt(3)/4 * 2^2 = sqrt(3) units^2.
To get the area of the hexagon, I need to multiply this by 6, since there are six triangles.
So the area of the hexagon is 6 * sqrt(3) units^2.