To calculate the slant height of the square pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, where one leg is the height of the pyramid and the other leg is half the length of the base.
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The side length of the base is 16, so half of the side length (the distance from the center of the base to the midpoint of a side) is: \[ \frac{16}{2} = 8 \]
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The height of the pyramid is given as 15.
Now we can use the Pythagorean theorem to find the slant height \( l \): \[ l = \sqrt{(\text{height})^2 + \left(\frac{\text{base side length}}{2}\right)^2} \] \[ l = \sqrt{(15)^2 + (8)^2} \] \[ l = \sqrt{225 + 64} \] \[ l = \sqrt{289} \] \[ l = 17 \]
Therefore, the slant height of the square pyramid is 17.
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