Question

In an equilateral triangle with side a prove that the area of the triangle is route 3 by 4 a square

Answer 1

By Heron's Formula

s=a+b+c/2=a+a+a/2=3a/2

s-a=3a/2-a=a/2

s-b=3a/2-a=a/2

s-c=3a/2-a=a/2

area of equilateral triangle=√[s(s-a)(s-b)(s-c)]

√(3a/2×a/2×a/2×a/2)

√(3a⁴/2⁴)

(√3)a²/4             proved