Question

show that the area of an equilateral triangle is root 3 by 4 a square where a is the side of the triangle ​

Answer 1

Answer: let us take an equilateral triangle with side a

then

according to heron's formula

semi perimeter = a+a+a/2 = 3a/2

area= √(s)(s-a)(s-a)(s-a)

√(3a/2)(a/2)(a/2)(a/2)

= √3a²/4