To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem. Since the slant height goes from the midpoint of one of the sides of the square base to the top of the pyramid, we can consider a right triangle formed by the slant height (the hypotenuse of the right triangle), half the length of the base (one of the legs of the triangle), and the height of the pyramid (the other leg of the triangle).
Let's denote:
- \( s \) as the slant height (given as 436.5 ft)
- \( h \) as the height of the pyramid (given as 321 ft)
- \( x \) as half the length of the base
Using the Pythagorean theorem:
\[ s^2 = h^2 + x^2 \]
Plugging in the values we have:
\[ (436.5)^2 = (321)^2 + x^2 \]
Now let's solve for \( x \):
\[ 190632.25 = 103041 + x^2 \]
\[ x^2 = 190632.25 - 103041 \]
\[ x^2 = 87591.25 \]
\[ x = \sqrt{87591.25} \]
\[ x \approx 295.96 \]
Now, remember, \( x \) is only half the length of the base, so to find the full length of the edge of the square base, we multiply \( x \) by 2:
\[ \text{Edge length of the base} = 2 \times x \]
\[ \text{Edge length of the base} \approx 2 \times 295.96 \]
\[ \text{Edge length of the base} \approx 591.92 \]
Rounded to the nearest tenth, the edge length of the square base is approximately 591.9 feet.