When calculating the lengths for a square based pyramid, is there a way to calculate the length from a point to the point opposite of it, given the side length and height?
Thanks in advanced.
of course there is. I assume by "opposite" you mean at the same height on the opposite slanting face.
If the base has side 2s, and the pyramid has height h, then If the point P is at height y, then it is at a distance x from the central axis of the pyramid. Using similar triangles,
x/s = (h-y)/h
The distance between P and P' is just 2x.
Of course, I may have misinterpreted what you want, but If so, just draw a diagram of your problem, and do the math.