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.