the square pyramid, is called so because its bottom is a square, in this case is a 12x12 square.
it has 4 triangular faces, we know the slant-height of the pyramid is 15, low and behold, it just so happen that the altitude or height of the triangular face is just that, 15. So we have 4 triangles then, each one with a height of 15, and a base of 12.
so, we simply get the area of the base and the triangles, sum them up, and that's the area of the pyramid.
[tex] \bf \stackrel{\textit{squarish base}}{(12\cdot 12)}~~+~~\stackrel{\textit{4 triangles}}{4\left[ \cfrac{1}{2}(12)(15) \right]}\implies 144+360\implies 504 [/tex]
