In geometryHeron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangleby requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

The following proof is trigonometric, and basically uses the cosine rule. First we compute the cosine squared in terms of the sides, and then the sine squared which we use in the formula A=1/2bc·sinA to derive the area of the triangle in terms of its sides, and thus prove Heron's formula. 

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