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Heron's Formula

Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.  In his work Metrika (On Measurement), written circa 60 CE, he presents a formula for the area of a triangle given the lengths of its three sides: \(a\), \(b\) and \(c\).

Area \( = \sqrt{s(s-a)(s-b)(s-c)}\) where \(s = \dfrac{a + b + c}{2}\).

Prove Heron's Formula is correct.

"Heron's Formula," Convergence (March 2007)