To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height, \( l \), is the hypotenuse of a right triangle formed by:
- The height of the pyramid (the distance from the apex to the center of the base).
- Half of the length of the base (which is half of the baseline).
Given:
- Point (height) = 12 inches
- Baseline (length of one side of the base) = 18 inches
First, we find half of the baseline:
\[ \text{Half of baseline} = \frac{18 \text{ in}}{2} = 9 \text{ in} \]
Now we can use the Pythagorean theorem:
\[ l = \sqrt{(\text{Height})^2 + (\text{Half of base})^2} \]
Substituting in the values:
\[ l = \sqrt{(12 \text{ in})^2 + (9 \text{ in})^2} \] \[ l = \sqrt{144 \text{ in}^2 + 81 \text{ in}^2} \] \[ l = \sqrt{225 \text{ in}^2} \] \[ l = 15 \text{ in} \]
Thus, the slant height of the square pyramid is 15 inches.
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