Wolfram Demonstrations Project

Let P be a point connected to and inside the vertices of a

-gon. Number the triangles counterclockwise from

. 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.

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

Contributed by: Jay Warendorff

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Total Areas of Alternating Subtriangles in a 2n-gon