Heron's formula


Heron's formula gives the area of a triangle when the lengths of all three sides are known. Given the lengths of the three sides of a triangle, a, b, c, the area of the triangle can be determined as

A = \sqrt{s(s-a)(s-b)(s-c)}

where s = \dfrac{a+b+c}{2} , semi-perimeter of the triangle.

The formula can be transformed to the following interesting forms.

A = \sqrt{s(s-a)(s-b)(s-c)}

\quad= \dfrac{1}{4}\sqrt{(a+b+c)(a+b-c)(a+c-b)(b+c-a)}

\quad= \dfrac{1}{4}\sqrt{[(a+b)+c)][(a+b)-c][c+(a-b)][(c-(a-b)]}







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