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Explain Heron's formula.
Heron’s Formula:
In 60 A.D, a great mathematician named Heron replaced the value “h” in terms of a, b, & c so, that height is not required to calculate the area of the triangle.
The formula given by Heron about the area of a triangle is also known as Heron’s Formula.
It is given as:
Area of triangle $ = \sqrt{s (s-a) (s-b)(s-c)}$
It is given as:-
$s = \frac{a+b+c}{2}$
For example,
Consider a triangle of sides 6,8 and 10.
First, we need to find semi perimeter, s
$s = \frac{6+8+10}{2} = \frac{24}{2} = 12$
Substitute 's ' and a,b,c in the formula,
$A= \sqrt{12 (12-6)(12-8)(12-10)}$
$A= \sqrt{12 \times 6 \times 4 \times 2}$
$A= \sqrt{576}$
$A = 24$ sq units.
displaystyle A=sqrt{12times 6times 4times 2}
displaystyle A=sqrt{576}
displaystyle A= 24unit^{2}