Question

An equilateral triangle has a height of `sqrt(6)` units. What is the area of the triangle?

Answer 1

Area: `=2sqrt(3)` sq. units

Explanation:

A common form for the equilateral triangle looks like:

If this common form is scaled up so that the height is `sqrt(6)`
then since `sqrt(6)=sqrt(3)xxsqrt(2)`
the scaled up base will have a length of `2 xx sqrt(2)` (or just `2sqrt(2)`
(and the height is the given value of `sqrt(6)`

The area of this (scaled up) triangle will be:
`"Area"=1/2 * "base" * "height"`

`color(white)("XXX")=1/2 * 2sqrt(2) * sqrt(6)`

`color(white)("XXX")=sqrt(12)`

`color(white)("XXX")=2sqrt(3)`