Question

A pyramid with a height of 15 and base length of 16

What is the slant height of this square pyramid?

answers:

14

8

17

289

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height can be defined as the hypotenuse of a right triangle where one leg is the height of the pyramid, and the other leg is half the length of the base.

Given:
- Height (h) = 15
- Base length (b) = 16

First, calculate half the base length:
\[
\text{Half base} = \frac{b}{2} = \frac{16}{2} = 8
\]

Now, we can use the Pythagorean theorem to find the slant height (l):
\[
l = \sqrt{(\text{Height})^2 + (\text{Half base})^2}
\]
Substituting the values:
\[
l = \sqrt{(15)^2 + (8)^2}
\]
Calculate the squares:
\[
l = \sqrt{225 + 64} = \sqrt{289}
\]
Taking the square root:
\[
l = 17
\]

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