### 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 congruent sides and six congruent angles of 120 degrees each.
To find the area of the hexagon, I can divide it into six equilateral triangles, each with a side length equal to the radius of the circle.
The area of one equilateral triangle is the square root of three over four times the side length squared.
So the area of one triangle is the square root of three over four times two squared, or the square root of three.
The area of the hexagon is six times the area of one triangle, or six times the square root of three.