To find out how much fencing Jamila needs to build a diagonal fence across her square 1-acre lot, we first need to determine the dimensions of the lot.
Since 1 acre is 43,560 square feet, and the lot is square-shaped, we can find the length of one side of the square by taking the square root of the area:
\[ \text{Side length} = \sqrt{43,560 \text{ square feet}} \approx 208.71 \text{ feet} \]
Next, we can use the Pythagorean theorem to find the length of the diagonal fence that she wants to build. The formula for the diagonal (\(d\)) of a square with side length \(s\) is:
\[ d = s\sqrt{2} \]
Substituting the side length (which we previously calculated):
\[ d = 208.71 \sqrt{2} \approx 208.71 \times 1.4142 \approx 295.5 \text{ feet} \]
Rounding to the nearest foot, we get:
\[ d \approx 296 \text{ feet} \]
Therefore, the amount of fencing Jamila needs to build the diagonal fence is 296 feet.