Let a, b, and a b denote the three edges of a triangle with lengths a, b, and c, respectively Use Lagrange 's Identity together with 2a b a 2 b 2 a b 2 to prove Heron 's Formula for the area A of a triangle, where s is the semiperimeter (a b c) 2 A Vs(s a)(s b)(s c)

Question: Let a, b, and a - b denote the three edges of a triangle with lengths a, b, and c, respectively. Use Lagrange's Identity together

Let a, b, and a - b denote the three edges of a triangle with lengths a, b, and c, respectively. Use Lagrange's Identity together with 2a ˆ™ b = ||a||2 + ||b||2 - ||a - b||2 to prove Heron's Formula for the area A of a triangle,

where s is the semiperimeter (a + b + c)/2.

A = Vs(s a)(s - b)(s - c)

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