Question

Math Help!! Geometry

Answer 1

So  hmmm if you notice the picture below

the bottom of the pyramid is a square, thus is called a "square pyramid"
so the sides are all the same, we know the are is 196, so we end up with a side of 14 for all

now, check the second picture in it, to get the "slant height" of the pyramid, or the height of the triangle, since we know the "lateral area" or the area of the sides is 448, well, the sides are just 4 triangles, divide that by 4, and you'd get the area of 1 triangle, or 112

anyhow, we get the slant height of the pyramid, or height of one triangle,
and notice the 3rd picture in it, is the right-triangle with the height of the pyramid, so, we use the pythagorean theorem to get the height of the pyramid

now, we know the base area is 196, and once you get the height "y", you'll have that as well

keeping in mind that   $\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height\\ ----------\\ B=196\\ h=y \end{cases}$