Max/Min Puzzles in Geometry III (2202.11211v3)

Abstract: The first two installments of this series of papers dealt with the maximum area polygons: Parallelogram, Rectangle, Square or Equilateral Triangle, in given triangles. Minimum area polygons were also considered in the second paper on Equilateral Triangles. In this paper the puzzle will be turned the other way around. Given the regular unit polygons, a Square, Pentagon, or Hexagon, we searched for the smallest area triangle(s) which contains it. The Dynamic Software Sketchpad v5.10 BETA was used for all examples and figures throughout the work.