Question

using heroes formula prove that the area of equilateral triangle with side is under root 3 a²/4​

Answer 1

Answer:

let the sides be a cm of equilateral triangle.

Step-by-step explanation:

s=(a+a+a)/2

s=3a/2.

according to heron's formula

area of triangle=

under root {s(s-a)(s-b)(s-c)}

so,underroot {3a/2(3a/2-a)(3a/2-a)(3a/2-a)}

so,under root {3a/2(a/2)(a/2)(a/2)}

=under root (power 4 of 3a / 16)

if we take it outside the root then,

=power 2 of 3a /4 .