In the square pyramid shown below, the diagonal length FC = 16√2 centimeters and the height of the pyramid is 7 centimeters. Find the slant height AD of the pyramid, to the nearest tenth. Show your work with reasoning for each step.
so since we know FC is 16sqrt2, the we know the side length is 16, 16^2 + 16^2 = (x)^2, x = 16sqrt2
then we use half the length of the square since we can make a triangle using the midpoint of the square.
7^2 + 8^2 = c^2, c = sqrt113 or roughly 10.63
Since the base is a square.....a side of the base = FC / sqrt (2) = 16
The slant height = sqrt [ (16 / 2)^2 + 7^2 ] = sqrt [ 8^2 + 7^2 ] = sqrt [ 64 + 49 ] =
sqrt [ 113 ] ≈ 10.6 cm
