To find the height \( h \) of the square pyramid using the Pythagorean Theorem, we need to consider the relationship between the height of the pyramid, the slant height, and half the length of the base.
Given:
- Slant height \( l = 25 \) feet
- Length of the base edge \( b = 40 \) feet
First, we can calculate half of the base edge: \[ \frac{b}{2} = \frac{40}{2} = 20 \text{ feet} \]
Now, we can apply the Pythagorean Theorem in the right triangle formed by the height \( h \), half the base edge \( 20 \) feet, and the slant height \( 25 \) feet: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \] Substituting the known values: \[ 25^2 = h^2 + 20^2 \] Calculating the squares: \[ 625 = h^2 + 400 \] To find \( h^2 \), we subtract \( 400 \) from \( 625 \): \[ h^2 = 625 - 400 = 225 \] Now take the square root to find \( h \): \[ h = \sqrt{225} = 15 \text{ feet} \]
Hence, rounded to the nearest tenth, the height \( h \) of the square pyramid is: \[ \boxed{15.0 \text{ ft.}} \]