Find the area of an equilateral triangle having each side `4c mdot`
In equilateral triangle ABC, `AB=BC=AC=a`
`s=1/2(a+a+a)`
`=3/2a`
now, ar`/_\ABC=sqrt(3/2a(3/2a-a)(3/2a-a)(3/2a-a))`
`=>sqrt(3/2axxa/2xxa/2xxa/2)`
`=>sqrt((a/2)^4xx3`
`=>a^2sqrt3/4` ​

Explanation

In equilateral triangle ABC, `AB=BC=AC=a`
`s=1/2(a+a+a)`
`=3/2a`
now, ar`/_\ABC=sqrt(3/2a(3/2a-a)(3/2a-a)(3/2a-a))`
`=>sqrt(3/2axxa/2xxa/2xxa/2)`
`=>sqrt((a/2)^4xx3`
`=>a^2sqrt3/4`