Step-by-step explanation:
the total surface area of such a pyramid is the sum of 5 sides :
1 bottom square (8×8)
4 side triangles (baseline 8, height 11.7)
the inner height of the pyramid we don't need, as the slant height is already given, and that is the height of the triangles of the wall of the pyramid.
the area of a triangle is
baseline × height / 2
if the slant height was unknown, we would have used the inner pyramid height and the side lengths to calculate the slant height.
so, we get a areas
bottom square = 8×8 = 64 in²
a side wall triangle = 8×11.7/2 = 4×11.7 = 46.8 in²
all 4 side triangles = 4×46.8 = 187.2 in²
so, the total surface area is
64 + 187.2 = 251.2 in²
