sir i want to know how to derive a formulae

This is the formula for area of an equilateral triangle with side 'a'.

The area of a triangle is half base x height.

In an equilateral triangle, we draw a perpendicular to the base, whih is a median and height of the triangle. Each angle is 60 degrees.

So using Pythagoras theorem, h² +(a/2)² =a²

Hence             h²= a² - (a/2)² = 3a²/4 

 

So h =root3a/2

Area of the triangle = (1/2) a h = (1/2)a (root 3 a/2)=(root3) a²/4