Question

Prove that the area of an equilateral triangle is equal to √3/4 a²  , where a is the side of the triangle.

Answer 1

Draw AD ⊥ BC 

⇒ ∆ABD ≅ ∆ACD [Br R.H.S.] 

∴ BD = DC [By cpctc] 

∴ BC = a 

∴ BD = DC = a/2

In right angled ∆ABD