Vol. 5, No. 3, 2012

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Vertex polygons

Candice Nielsen

Vol. 5 (2012), No. 3, 361–369

We look at hexagons whose vertex triangles have equal area, and identify necessary conditions for these hexagons to also have vertex quadrilaterals with equal area. We discover a method for creating a hexagon whose vertex quadrilaterals have equal area without necessarily having vertex triangles of equal area. Finally, we generalize the process to build any polygon with an even number of sides to have certain vertex polygons with equal area.

vertex polygons, vertex triangles, vertex quadrilaterals, geometry, equal area, hexagon, proof by contradiction
Mathematical Subject Classification 2010
Primary: 51N20
Secondary: 00A99
Received: 18 September 2012
Revised: 10 November 2012
Accepted: 15 December 2012
Published: 14 April 2013

Communicated by Colin Adams
Candice Nielsen
Mathematics Department
Elmhurst College
Elmhurst, IL 60126
United States