Graphs of area versus side lengths for Regular Polygons

Change the size of the triangle by dragging point A. Point P is the coordinates (side length, area) as the triangle changes size. What type of function does this appear to be?
Now drag the slider labeled "n" to try to match the tracing of point P with a function. What appears to be the function that represents the area in terms of side length?
Do the same with the square and the regular pentagon, changing their size by dragging a vertex. Points Q and R will trace the side length versus the area. What is different about the three different curves? What is similar?