Question

In a equilateral triangle with side.A prove that area of triangle is

Answer 1

Answer:

As per the question obove we let the side of triangle be A

Now ,perimeter of triangle is = a+a+a

a+a+a= 3a

therefore ,semi-perimeter =a+b+c/2

= 3a/2. so, s=a+b+c/2

now , Area of triangle by heron's formula = √s(s-a)(s-b)(s-c)

so,√3a/2(3a/2-a)(3a/2-a)(3a/2-a)

= √3a/2(a/2)(a/2)(a/2)

= √3a^4/16

= √3a^2/4

= hence, It is proved that area of triangle is equal to √3a^2/4