Notice the first picture here
to get the height of the box, or triangular prism,
you need to find the "altitude" of the triangle,
and for that, you can simply use the pythagorean theorem,
notice, as 17 is the slanted or hypotenuse side,
and 8 is the base, or half 16
now, how much cardboard? meaning, how much is the
surface are of that triangular prism
notice the 2nd picture here
the prism is really just 3 rectangles and 2 triangles,
stacked up at each other at the edges, so
split them up, find their independent areas,
recall area of a triange = 1/2 b*h
and them SUM them up
and that's the surface area of that triangular prism,
and thus the box, and that's how much cardboard
was used