# Triangles with Equal Area Are Equidecomposable (Equivalent by Dissection)

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A dissection of a polygon is a set of polygons that cover exactly without gaps or overlaps. Two polygons are equidecomposable (or equivalent by dissection) if there is a dissection of one that can be reassembled to form the other. In 2D, two polygons of equal area are equidecomposable. On the other hand in 3D, even the cube and the tetrahedron of equal volume are not equidecomposable.

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Contributed by: Izidor Hafner (May 2017)

Open content licensed under CC BY-NC-SA

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Reference

[1] B. I. Agrunov and M. B. Balk, *Elemenarnaja Geometrija* (in Russian), (*Elementary Geometry*), Moscow 1966, pp. 174–175.

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