Question

how do you find the slant height of a square pyramid when you know the base length and the surface area

Answer 1

By surface area you mean area, right? If so, then you know (base*height)/2=area so work backwards. Do area*2 and divide by base. Now you have the height, but you want the slant height. Use Pythagorean Theorem, a^2+b^2=c^2. So, base^2+height^2=slant height^2. Plug in the numbers to the equations I gave you and you get your answer.