Prove that the area of an equilateral triangle is equal to `(sqrt(3))/4a^2,` where `a` is the side of the triangle. GIVEN : An equilateral triangle `A B C` such that `A B=B C=C A=adot` TO PROVE : `a r( A B C)=(sqrt(3))/4a^2` CONSTRUCTION : Draw `A D_|_B Cdot`

Explanation

a is the side of traingle .

`s=(a+a+a)/2=(3a)/(2)`

now use heron's formula ,

area of traingle `=sqrt {(3a)/(2) {(3a)/(2)-a)((3a)/(2)-a)((3a)/(2)-a)}=sqrt {(3a)^4/16}`

=`sqrt (3/4) .a^2` (hence proved)