Assume you inscribe a regular hexagon inside a circle of radius $r$, as shown by the green hexagon in this Figure:

(The yellow hexagon circumscribes the circle.) The area of the inscribed hexagon is $A=$ . A hexagon is a polygon with six sides. A regular hexagon is a hexagon where all sides and all interior angles are equal. A regular hexagon inscribed in a circle is the largest regular hexagon that fits in the circle. Think of the hexagon as consisting of 6 equilateral triangles. Use the formula for the area of an equilateral triangle.