Question

Prove that area of an equilateral triangle of side a is √3a^2/4

Explain plz​

Answer 1

Answer:

Here u go

Step-by-step explanation:

Answer 2

Let the side of an equilateral triangle be "a".

According to Heron's formula,

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

• Here, a,b and c refers to the equal sides of triangle
• S = semi perimeter = ( a+b+c )/2

And in equilateral triangle, a = b = c

Then, S = a+a+a/2 = 3a/2

Now,

The area of equilateral triangle will be,

⇒ area = √[s( s-a )( s-b )( s-c )]

⇒area = √[3a/2 (3a/2 - a) (3a/2 - a) (3a/2 - a)]

⇒ area = √3a/2 [(a/2) × (a/2) × (a/2)]

⇒ area = √(3a^4 / 16)

⇒ area of equilateral triangle = (√3)a^2/4

Hence Proved!