## Outer-Inner Polygon Area Ratios

For a quadrilateral (depicted below), in the case of joining each vertex to the midpoint of the next but one edge (all done clockwise or all done counter-clockwise) it is easy to be misled by rounding errors into believing that the ratio of the areas of the outer to inner quadrilaterals is 5. In fact it lies between 5 and 6.

There is an applet for displaying the diagrams for this paper and for assisting in the exploration can be found here.