Question

find the area of an equilateral triangle in one side is √3a square /4 by using herons formula

Answer 1

Answer:

Hello.  Hope this helps you.

Heron's Formula tells us that the area is given by

A² = s (s-a) (s-b) (s-c)

[ written with A² just to avoid ugly √ signs ].

As we have an equilateral triangle, a = b = c, so this simplifies to

A² = s ( s-a )³

The semiperimeter s is

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

so

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

Putting this into the formula for A², we get

A² = s ( s-a )³ = ( 3a/2) × (a/2)³ = 3 a⁴ / 2⁴

=> A = √3 a² / 4