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Triangle Squaring

TriangleSquaring

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then

area(DeltaABC)=1/2AB·CD=AB·DE,

and ABFG can be squared by rectangle squaring. The general polygon can be treated by drawing diagonals, squaring the constituent triangles, and then combining the squares together using the Pythagorean theorem.

See also

Pythagorean Theorem, Rectangle Squaring, Squaring

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References

Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 14-15, 1990.

Referenced on Wolfram|Alpha

Triangle Squaring

Cite this as:

Weisstein, Eric W. "Triangle Squaring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangleSquaring.html

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