In an equilateral triangle with side a, prove that area = .

Question

Philoid · Accepted Answer

Let ∆ ABC be an equilateral triangle with side a.

To prove: Area of ∆ ABC =

In ∆ ABC, AD bisects BC

Now, in ∆ ACD

Using Pythagoras theorem,

AC² = AD² + DC²

⇒ AD² = AC² – DC²

Now, in ∆ ABC

Area of ∆ ABC =