Question

Find the slant height of a square pyramid if 15 is the height and 8 is the base

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean theorem.

First, let's find the length of the diagonal of the base of the pyramid.
Since the base is a square, all sides are equal. Therefore, the length of one side of the base is 8.

Using the Pythagorean theorem, we can find the diagonal of the base:
diagonal^2 = side^2 + side^2
diagonal^2 = 8^2 + 8^2
diagonal^2 = 64 + 64
diagonal^2 = 128
diagonal = √128
diagonal ≈ 11.31

Now, let's find the slant height of the pyramid.
The slant height is the hypotenuse of a right triangle, with the height of the pyramid as one leg and the diagonal of the base as the other leg.

Using the Pythagorean theorem again:
slant height^2 = diagonal^2 + height^2
slant height^2 = (11.31)^2 + 15^2
slant height^2 = 128 + 225
slant height^2 = 353
slant height = √353
slant height ≈ 18.80

Therefore, the slant height of the square pyramid is approximately 18.80.