To determine how much fencing Jamila needs to split her 1-acre square lot diagonally, we first need to calculate the length of the diagonal of the square.
Since the lot is a square and each side is 209 feet long, we can use the Pythagorean theorem to find the length of the diagonal \(d\):
\[ d = \sqrt{side^2 + side^2} = \sqrt{209^2 + 209^2} = \sqrt{2 \cdot 209^2} = 209\sqrt{2} \]
Now we calculate \(209\sqrt{2}\): \[ \sqrt{2} \approx 1.414 \]
Therefore: \[ d \approx 209 \times 1.414 \approx 295.806 \]
Rounding \(295.806\) to the nearest foot, we get \(296\) feet.
Thus, Jamila needs 296 feet of fencing.