Demonstration 4. Infinite area ratios for non-convex pentagons

In this demo, you will see a pentagon and its related midpoint polygon. You can move the yellow vertex of the pentagon around, and see how this affects the relevant areas. By moving the point in close to the left-most point of the figure, you should be able to get the midpoint polygon to have greater area that the original polygon!

In fact, if you put the point in exactly the right spot, you could get an infinite area ratio, as the area of the original polygon would be precisely zero.