Question

there is a square pyramid, the middle of it is 15 and the base is 16. what is the slant height of this square pyramid.



14

8

289

17

Answer 1

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

In this case, we know:

- The height (h) of the pyramid from the base to the apex (middle) is 15 units, and
- The base of the pyramid is a square with side length 16 units.

The base's half diagonal can be calculated using:

1. The side length of the base is 16 units, so the distance from the center of the base to a vertex of the base (which forms a right triangle with the slant height) can be calculated as half the side length:

\[
\text{Half base length} = \frac{16}{2} = 8 \text{ units}
\]

Now, we can use the height (15 units) and the half base length (8 units) to find the slant height (l) of the pyramid using the Pythagorean theorem.

\[
l^2 = h^2 + \left(\text{Half base length}\right)^2
\]

Substituting the values:

\[
l^2 = 15^2 + 8^2
\]
\[
l^2 = 225 + 64
\]
\[
l^2 = 289
\]

Now, take the square root of both sides to solve for l:

\[
l = \sqrt{289} = 17 \text{ units}
\]

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