Question

Find the slant height of the square pyramid.

(1 point)
height=15
width=16

Answer 1

To find the slant height (\( l \)) of a square pyramid, you can use the Pythagorean theorem. The slant height forms a right triangle with half of the base width and the height of the pyramid.

1. The base width is 16, so half of the base width is:
\[
\frac{16}{2} = 8
\]

2. The height of the pyramid is 15.

3. Now, we can use the Pythagorean theorem, which states that in a right triangle:
\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]
Substituting the height \( h = 15 \) and half of the base width \( \frac{b}{2} = 8 \):
\[
l^2 = 15^2 + 8^2
\]
\[
l^2 = 225 + 64
\]
\[
l^2 = 289
\]

4. Now take the square root to find the slant height:
\[
l = \sqrt{289} = 17
\]

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