Uncommon

Heron's formula

Triangle area in terms of side lengths

Heron's formula

Uncommon card · No. 89589

In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths ⁠a,⁠ ⁠b,⁠ ⁠c.⁠ Letting ⁠s⁠ be the semiperimeter of the triangle, ⁠s=12(a+b+c)⁠, the area ⁠A⁠ is A=s(s−a)(s−b)(s−c). It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work Metrica, though it was probably known centuries earlier.

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