1. **Problem statement:** Find the perimeter of the square with vertices at (0,0), (4,5), (0,9), and (-4,5). 2. **Formula:** The perimeter $P$ of a square is given by $P = 4s$, where $s$ is the length of one side. 3. **Find the length of one side:** Calculate the distance between two adjacent vertices, for example, between (0,0) and (4,5). 4. **Distance formula:** The distance $d$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 5. **Calculate side length:** $$s = \sqrt{(4 - 0)^2 + (5 - 0)^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41}$$ 6. **Simplify:** $s = \sqrt{41} \approx 6.4031$ 7. **Calculate perimeter:** $$P = 4s = 4 \times 6.4031 = 25.6124$$ 8. **Round to 1 decimal place:** $P \approx 25.6$ **Final answer:** The perimeter of the square is $25.6$ units.