Regular Polygons and Equivalent Triangles
Two geometric figures are equidecomposable if each can be partitioned into the same finite number of parts that are pairwise congruent.
Equidecomposability is an equivalence relation, and each class is called an area.
This means that two equidecomposable figures are equivalent, that is they have the same area.
Start the animation and discover a visual proof of the equidecomposability of a regular pentagon with the equivalent triangle.
A question...
Any regular polygon can be either inscribed in or circumscribed about a circle. What can you say about the height of the triangle equivalent to a regular polygon, if you consider the circumscribed circle, rather than the inscribed one, as the reference?
... Another Question
Can we say the same holds for every cyclic polygon, not necessarily regular? Explain your reasoning.