Question

heros formula explain me
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Answer 1

Heron's Formula:

Heron's formula is used to find the area of the triangle when all its three sides are given.

Herons Formula:

$\sqrt{s(s - a)(s - b)(s - c)}$

where,s is semi-perimeter and a, b and c are the sides of the triangle.

Semi-perimeter:

Its the half of the perimeter of the triangle.

$s = \frac{a + b + c}{2}$

Example:

Find the area of triangle with sides 13cm, 14cm and 15cm.

$a = 13cm , b = 14cm , c = 15cm \\ s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21cm \\ Area = \sqrt{s(s - a)(s - b)(s - c)} \\ Area = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} \\ Area = \sqrt{21 \times 8 \times 7 \times 6} \\ Area = \sqrt{7056} \\ Area = 84c {m}^{2}$

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