Question

How do I find lateral height with only surface area and length of the edge?

Answer 1

I'm guessing you are talking about the surface area of a cone?
Also by length of the edge, do you mean slant height?
Here is the area formula for a cone:
Lateral Area = (π • r • slant height)
Solving for "r" we get:

radius = Lateral Area / (π • slant height)

When you calculate the radius, you can solve for the height by
height^2 = slant height^2 - radius^2