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.
-
The base width is 16, so half of the base width is: \[ \frac{16}{2} = 8 \]
-
The height of the pyramid is 15.
-
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 \( \frac{b}{2} = 8 \): \[ l^2 = 15^2 + 8^2 \] \[ l^2 = 225 + 64 \] \[ l^2 = 289 \]
-
Now take the square root to find the slant height: \[ l = \sqrt{289} = 17 \]
Thus, the slant height of the square pyramid is 17.