Question

12 in.
18 in.
Find the slant height of the square pyramid. Round to the
nearest whole inch, if necessary.

Answer 1

To find the slant height of a square pyramid, we need to use the Pythagorean theorem. The slant height (l) can be found from the height (h) of the pyramid and half the length of the base (a).

In this case:
- The height of the pyramid (h) is 12 inches.
- The side length of the base (a) is 18 inches.

First, we need to find half of the base length:
\[
\frac{a}{2} = \frac{18\, \text{in}}{2} = 9\, \text{in}
\]

Now, we can apply the Pythagorean theorem:
\[
l = \sqrt{h^2 + \left(\frac{a}{2}\right)^2}
\]
Substituting the values:
\[
l = \sqrt{12^2 + 9^2}
\]
Calculating the squares:
\[
l = \sqrt{144 + 81}
\]
\[
l = \sqrt{225}
\]
Calculating the square root:
\[
l = 15\, \text{in}
\]

Thus, the slant height of the square pyramid is **15 inches**.