Heron's Formula

Eric W. Weisstein
January 11, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/HeronsFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HeronsFormula.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Check

s=(a+b+c)/2;
A=Sqrt[s(s-a)(s-b)(s-c)];

Simplify[A-Sqrt[2(a^2b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)]/4]

Simplify[A-Sqrt[(a+b+c)(-a+b+c)(a-b+c)(a+b-c)]/4]

Simplify[A-Sqrt[(2a b)^2-(a^2+b^2-c^2)^2]/4]