1. **State the problem:** We need to find the perimeter of a rectangle with vertices at approximately $(-2, -1)$, $(4, 1)$, $(5, -1)$, and $(-1, -4)$ on the coordinate plane. The rectangle is tilted, so we cannot simply use length and width from the axes. 2. **Formula for perimeter of a rectangle:** $$\text{Perimeter} = 2(\text{length} + \text{width})$$ We need to find the lengths of two adjacent sides (length and width). 3. **Calculate the length of one side:** Choose two adjacent vertices, for example, $(-2, -1)$ and $(4, 1)$. Use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Calculate: $$d = \sqrt{(4 - (-2))^2 + (1 - (-1))^2} = \sqrt{6^2 + 2^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10} \approx 6.3246$$ 4. **Calculate the length of the adjacent side:** Choose vertices $(4, 1)$ and $(5, -1)$. Calculate: $$d = \sqrt{(5 - 4)^2 + (-1 - 1)^2} = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.2361$$ 5. **Calculate the perimeter:** $$\text{Perimeter} = 2(6.3246 + 2.2361) = 2(8.5607) = 17.1214$$ 6. **Round to 1 decimal place:** $$17.1$$ **Final answer:** The perimeter of the rectangle is approximately $17.1$ units.