Montramugdha is using "Heron's formula" (
https://en.wikipedia.org/wiki/Heron%27s_formula):
Given sides of length a, b, and c, let s be the "semi-perimeter", [tex]s= \frac{a+ b+ c}{2}[/tex].
Then the area is given by [tex]A= \sqrt{s(s-a)(s-b)(s-c)}[/tex].
In the example initially given, a= 3, b= 4, c= 5, [tex]s= \frac{3+ 4+ 5}{2}= 6[/tex] so the area is [tex]A= \sqrt{6(6-3)(6-4)(6-5)}= \sqrt{6(3)(2)(1)}= \sqrt{36}= 6[/tex] which is, of course, the same as (3)(4)/2 since this is a right triangle.
If we were given an equilateral triangle with side lengths all 4, we could find the area by dividing it into two right triangles with hypotenuse of length 4, one leg of length 2, so the other leg of length [tex]\sqrt{4^2- 2^2}= \sqrt{12}= 2\sqrt{3}[/tex]. Each right triangle has area [tex]\frac{2(2\sqrt{3}}{2}= 2\sqrt{3}[/tex] and the original equilateral triangle has area [tex]4\sqrt{3}[/tex].
By Heron's formula, [tex]s= \frac{4+ 4+ 4}{2}= 6[/tex] so the area is [tex]A= \sqrt{6(6-4)(6-4)(6-4)}= \sqrt{6(2)(2)(2)}= \sqrt{48}= \sqrt{3(16)}= 4\sqrt{3}[/tex].