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plz state and proof herons formula in step by step explanation which i can understand i m in class 10
In geometry, Heron's (or Hero's) formula, named after Heron of Alexandria, states that the area A of a triangle whose sides have lengths a, b, and c is
where s is the semiperimeter of the triangle:
Proof
A modern proof, which uses algebra and is quite unlike the one provided by Heron (in his book Metrica), follows. Let a, b, c be the sides of the triangle and A, B, C the angles opposite those sides. We have
by the law of cosines. From this proof get the algebraic statement:
The altitude of the triangle on base a has length b·sin(C), and it follows
The difference of two squares factorization was used in two different steps?.
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