Question

What is the area of an equilateral triangle, with apothem of 6 inches in length?

Answer 1

`color(white)(xx)12sqrt3`

Explanation:

`color(white)(xx)sqrt3/2a=h`

`=>sqrt3/2a=6`
`=>color(red)(2/sqrt3*)sqrt3/2a=color(red)(2/sqrt3*)6`
`=>a=(2color(blue)(*sqrt3))/(sqrt3color(blue)(*sqrt3))*6`

`=>a=4sqrt3`

`color(white)(xx)A=(ah)/2`
`color(white)(xxxx)=6*4sqrt3/2`
`color(white)(xxxx)=12sqrt3`