How to find the area of a equalateral triangle using the height?

If the side of the triangle is a, the height is given by √a²-a²/4=√(¾a²)=a√3/2.
So if you know the height, h, work out 2h/√3 to find the side a.
The area is ½ah=½(2h/√3)h=h²/√3 which can be written h²√3/3.