Midpoint Polygons

The Solution
   
  • Triangles: The Base Case
    •    
  • Convex Quadrilaterals
       
  • Non-Convex Quadrilaterals*
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  • Self-Intersecting Quadrilaterals*
    •    
  • Convex Pentagons
    •    
  • Convex Hexagons And Up
       
  • The General Case*

    • Pedagogy
       
  • Math 104
       
  • Original Discussion
    •    
  • Oriented Area Part 1
    •    
  • Oriented Area Part 2
    •    
  • Vector Notation

    • Java Demonstrations
       
  • Area of Midpoint Triangles
    •    
  • Area of Midpoint Quadrilaterals
    •    
  • Area Max for Convex Pentagons
    •    
  • Infinite Area Ratios
    •    
  • Star Pentagons
    •    
  • Non-Midpoint Polygons

    • Bibliography

    Triangles: The Base Case

    Summary

    • The area ratio for triangles is always 1/4.

    Congruent Triangles

    The first example, familiar to most students, concerns a triangle. The midpoint polygon divides the triangular region up into four congruent triangles so the area ratio is 1/4.


    Demonstration 1. Area ratio for midpoint triangles.
    (Click on the picture or caption to go to the demonstration.)



    Problem -- Solution -- Pedagogy -- Demos -- Bibliography