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## Answers

**In geometry**

**,**

**Heron's formula**

**(sometimes called Hero's formula), named after**

**Hero of Alexandria,**

**gives the**

**area**

**of a**

**triangle**

**by 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.**