Question

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define herons formula​

Answer 1

Answer:

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and formula of herons is

Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is

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

where s is the semi-perimeter of the triangle; that is,

{\displaystyle s={\frac {a+b+c}{2}}.}[2]

Heron's formula can also be written as

{\displaystyle A={\frac {1}{4}}{\sqrt {(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}}}{\displaystyle A={\frac {1}{4}}{\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}}{\displaystyle A={\frac {1}{4}}{\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}}{\displaystyle A={\frac {1}{4}}{\sqrt {4(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{2}+b^{2}+c^{2})^{2}}}}{\displaystyle A={\frac {1}{4}}{\sqrt {4a^{2}b^{2}-(a^{2}+b^{2}-c^{2})^{2}}}.}