This applet that deals with a regular pentagon is an extension of two[br]earlier applets - "Point in an Equilateral Triangle" and "Point in a Square".[br][br][b][i][br]You can adjust the size and orientation of the pentagon by dragging[br]the small white dots.[/i][/b][br][br][br]After exploring the earlier applets as well as this one, what can you say about sum of the [br]distances from a point in the interior of the pentagon to each of the sides? Why is this true?[br][br][br]Can you devise a way to deal with the cases in which the sum of the distances is undefined?[br][br][br]What is the shape of the region for which the sum is fixed?[br][br][br]Under what circumstances can you form a new pentagon using the five distances to the sides?[br][br][br]Can a similar result be obtained for any regular polygon with an odd number of sides?[br][br][br]What about polygons with an even number of sides?