Question

Use the image to answer the question. The image depicts a square pyramid with a line going down the middle. That line is labeled 15. One of the bottom sides is labeled 16. Find The slant height of the square pyramid.

Answer 1

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

The slant height is the hypotenuse of a right triangle with one leg being half of the diagonal of the base (8) and the other leg being the slant height of one of the triangular faces.

Using the Pythagorean theorem:

(8)^2 + (slant height)^2 = (15)^2
64 + (slant height)^2 = 225
(slant height)^2 = 225 - 64
(slant height)^2 = 161
slant height = √161 ≈ 12.69

Therefore, the slant height of the square pyramid is approximately 12.69.