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 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.

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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?