Question

If the height of the pyramid is 15 and the length is 16 what is the slant height of this square pyramid?

Answer 1

To find the slant height of a square pyramid, you can use the Pythagorean theorem. In a square pyramid, the slant height \( l \) can be found using the formula:

\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]

where:
- \( h \) is the height of the pyramid,
- \( b \) is the length of the base (the side length of the square).

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

First, calculate half of the base length:

\[
\frac{b}{2} = \frac{16}{2} = 8
\]

Now, substitute these values into the slant height formula:

\[
l = \sqrt{15^2 + 8^2}
\]

Calculating \( 15^2 \) and \( 8^2 \):

\[
15^2 = 225
\]
\[
8^2 = 64
\]

Now add these values:

\[
l = \sqrt{225 + 64} = \sqrt{289}
\]

Finally, take the square root:

\[
l = 17
\]

Thus, the slant height of the square pyramid is \( \boxed{17} \).