To find the length of the edge of the square base of the pyramid, we can use the relationship between the height, the slant height, and the dimensions of the base.
We can visualize the situation as follows:
- The height of the pyramid (h) is 321 feet.
- The slant height (l) is given as 436.5 feet.
For a pyramid with a square base, you can draw a right triangle that includes:
- The height (h) of the pyramid,
- Half the length of the edge of the square base (let's call this \( \frac{b}{2} \), where \( b \) is the length of the edge of the square base),
- The slant height (l) as the hypotenuse of the triangle.
From the right triangle we can use the Pythagorean theorem:
\[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \]
Plugging in the known values:
\[ (436.5)^2 = (321)^2 + \left(\frac{b}{2}\right)^2 \]
Calculating the squares:
\[ 190,590.25 = 103,041 + \left(\frac{b}{2}\right)^2 \]
Now, isolate \( \left(\frac{b}{2}\right)^2 \):
\[ \left(\frac{b}{2}\right)^2 = 190,590.25 - 103,041 \]
\[ \left(\frac{b}{2}\right)^2 = 87,549.25 \]
Now take the square root of both sides:
\[ \frac{b}{2} = \sqrt{87,549.25} \]
Using a calculator, we find:
\[ \frac{b}{2} \approx 296.2 \]
Now, multiply by 2 to find \( b \):
\[ b \approx 2 \times 296.2 \approx 592.4 \]
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is:
\[ \boxed{592.4 \text{ ft}} \]