Question

In an equilateral triangle with side a.Prove that the area of the triangle is √3by 4 a square.

Answer 1

Let the side of triangle be a.

Now, Semiperimeter of triangle = (a + a + a)/2 = 3a/2

Area of triangle by Heron's formula = square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root
Now, s - a = (3a/2) - a = a/2

And, a = b = c = a (Equilateral triangle)

Thus, Area =