Question

How do you find the area of an equilateral triangle with an apothem of `4sqrt3`?

Answer 1

`144sqrt3`

Explanation:

(source: wolfram.com)

`color(white)(xx)tan30=sqrt3/3`

`=>(4sqrt3)/(a/2)=sqrt3/3`
`=>color(red)((a/2)*2*1/sqrt3*3)(4sqrt3)/(a/2)=color(red)((a/2)*2*1/sqrt3*3)sqrt3/3`
`=>a=24`

`A=1/4sqrt3*24^2`
`color(white)(xx)=144sqrt3`