boundaries & enclosures

A GREEN polygonal region has a BLUE polygonal boundary. Purple dots control sizes and orientation of the polygons. Purple slider in right hand panel controls the number of sides. Drag the yellow dot along the dotted line to vary the relative sizes of the GREEN and BLUE regions. How do the graphs in the right hand panel as you vary the - - number of sides? - the relative sizes of the green and blue regions? Write expressions for these two functions. What questions could / would you put to your students based on this applet?