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Total Areas of Alternating Subtriangles in a 2n-gon


	Let P be a point connected to and inside the vertices of a -gon. Number the triangles counterclockwise from to . Then the sum of the areas of the even-numbered triangles is equal to the sum of the areas of the odd-numbered triangles. Drag the point P to change the figure.


	Contributed by: Jay Warendorff

A generalization of problem 4.28 in Problems in Plane and Solid Geometry v.1 Plane Geometry by Viktor Prasolov.

Area (Wolfram MathWorld)

Polygon (Wolfram MathWorld)

Triangle (Wolfram MathWorld)

"Total Areas of Alternating Subtriangles in a 2 n -gon" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TotalAreasOfAlternatingSubtrianglesInA2nGon/

Contributed by: Jay Warendorff

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