Rubber Band Perimeter

Rubber Band Perimeter

Below there are 7 points with a tight rubber band wrapped around all of them, creating a shape.  The points can be moved, but notice that they lock to places where two gridlines meet.  For this puzzle, you will be moving the points, but you are only allowed to move them to places where they lock. The rubber band currently has a perimeter of 24 units.  Drag the points around to make new shapes.  Try to create other shapes with a perimeter of exactly 24.  The perimeter is displayed in the upper left hand corner.

Extensions

  1. Try to make a perimeter of 24 using exactly 3 points as vertices?  How about exactly 4, 5, 6, 7?  Are they all possible?
  2. Try to make a perimeter of 24 where at least one of the sides has an irrational length?  Is it possible?
  3. Pick a perimeter other than 24.  Can you make that perimeter with 3, 4, 5, 6, or 7 points?
  4. What is the largest perimeter you can make using 3 points? 4? 5? 6? 7?
  5. What othewr extensions can you think of?