A regular hexagon and an equilateral triangle have the same perimeter. What is the ratio of their areas?
The side of the hexagon is half that of the triangle. The hexagon can be divided, starting from the center, into six equilateral triangles, whose side is therefore half that of the triangle. Thus, their area is one quarter of its own, and the area of the hexagon is $6 / 4 = 3 / 2$ of that of the equilateral triangle.