Find the slant height of the square pyramid. The lengths are 16 and 15

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean Theorem on a right triangle formed by the slant height, the height of the pyramid, and half the length of the base.

In this case, the base of the pyramid is a square with sides measuring 16. Therefore, half the length of the base is 8.

We can let the height of the pyramid be h.

Using the Pythagorean Theorem, we have:
h^2 + 8^2 = slant height^2

h^2 + 64 = slant height^2

We also know the height of the pyramid is 15, so:
15^2 + 64 = slant height^2

225 + 64 = slant height^2
289 = slant height^2

Taking the square root of both sides, we find the slant height is √289 = 17.

Therefore, the slant height of the square pyramid is 17 units.