Equidecomposition of a Triangle and a Rectangle II

A triangle is equidecomposable with a rectangle. Based on such a decomposition one can easily obtain the basic formula for the Area of Parallelogramarea of a triangle: base × altitude = twice the area. But there are great many ways to find the area of a triangle. One of the rather more common - area = semiperimeter × inradius - is also easily demonstrated by a simple decomposition. (Douglas Rogers who has suggested creating the demonstration used it in his proof of the Pythagorean proposition. He also observed that one implication of this formula is that in a triangle with rational sides and area, the inradius is also rational.)

Equidecomposition by Dissection

1. Carpet With a Hole
2. Equidecomposition of a Rectangle and a Square
3. Equidecomposition of Two Parallelograms
4. Equidecomposition of Two Rectangles
5. Equidecomposition of a Triangle and a Rectangle
6. Equidecomposition of a Triangle and a Rectangle
7. Perigal's Proof of the Pythagorean Theorem
8. Two Symmetric Triangles Are Directly Equidecomposable
9. Wallace-Bolyai-Gerwien Theorem

Copyright © 1996-2009 Alexander Bogomolny