To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem.
Let:
- \( h \) be the height of the pyramid (321 ft),
- \( l \) be the slant height (436.5 ft),
- \( a \) be half of the length of the edge of the base.
The relationship between the height of the pyramid, the slant height, and half the base edge can be expressed as:
\[ l^2 = h^2 + a^2 \]
Substituting the known values into the equation, we get:
\[ 436.5^2 = 321^2 + a^2 \]
Calculating \( 436.5^2 \):
\[ 436.5^2 = 190,119.25 \]
Calculating \( 321^2 \):
\[ 321^2 = 103,041 \]
Now substituting these values back into the equation:
\[ 190,119.25 = 103,041 + a^2 \]
To find \( a^2 \), we rearrange the equation:
\[ a^2 = 190,119.25 - 103,041 \] \[ a^2 = 87,078.25 \]
Now, we take the square root to find \( a \):
\[ a = \sqrt{87,078.25} \approx 294.5 \]
Since \( a \) represents half of the length of the edge of the base, we can find the full length \( b \):
\[ b = 2a = 2 \times 294.5 \approx 589.0 \]
Thus, the length of the edge of the square base is approximately:
\[ \boxed{589.0} \text{ ft} \]