Find the area of a circle circumscribed about a regular 6-gon with a side of 3 cm.

Since the hexagon is regular, its vertices divide the circle into six equal arcs. The degree measure of the full circle is 360, then the arc AB = 360/6 = 60.

Let’s construct the radii ОА and ОВ.

In the triangle AOB AB = BC = R, the central angle AOB rests on the arc AB = 60, then the angle AOB = 60, and then the triangle AOB is equilateral.

AB = ОА = ОВ = R = 3 cm.

Determine the area of the circle.

S = π * R2 = 9 * π cm2.

Answer: The area of the circle is 9 * π cm2.