JSXGraph example

# Total Areas of Alternating Subtriangles in a n-gon with n=2m

Let P be a point connected to and inside the vertices of a 2m-gon. Number the triangles counterclockwise from 1 to 2n. 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 or change with the radio buttons the number of vertices.

n = | 6 | 8 | 10

1 | 2