Drag the slider to the right to increase the number of sides in the regular polygon.

The orange line is the diagonal from vertex to opposite vertex.

The red line joins the mid-points of opposite sides

The calculations show the results when the perimeter of the shape is divided by the length of the orange line and then when it is divided by the length of the red line.

When there are 4 sides (n = 4), which line is longer?

What happens to the lengths of the lines as the number of sides increases?

What happens to the polygon as the number of sides increases? What does it start to look like?

What happens to the two calculations as the number if sides increases?