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Given a convex polygon with 4 or more sides, is there a way to transform (convert, reduce) that polygon to a triangle having the same area as the polygon by using only a compass and straight edge?

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    You may be interested in the [Bolyai-Gerwien Theorem.](http://en.wikipedia.org/wiki/Wallace%E2%80%93Bolyai%E2%80%93Gerwien_theorem) All the constructions can be done with compass and straightedge.2012-09-29

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