Question

What is the slant height of a square pyramid that has a surface area of 336 square meters and a side length of 12

Answer 1

Check the picture below.

the surface area of the pyramid is simply the area of the four triangular faces plus the squarish base, and the triangular faces have a base of 12 and an altitude or height of "s", and we know that's 336.

$336~~ = ~~\stackrel{\textit{\LARGE Areas}}{\stackrel{square}{(12)(12)}~~ + ~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(\underset{b}{12})(\underset{h}{s}) \right]}}\implies 336~~ = ~~144~~ + ~~24s \\\\\\ 192=24s\implies \cfrac{192}{24}=s\implies 8~m=s$