Find the area and perimeter of the figure determined by the points. (-4,-1),(-1,5),(8,5)(5,-1)

1. **Determine the area using Shoelace formula:**
A = \frac{1}{2} \left| (-4 \cdot 5) + (-1 \cdot 5) + (8 \cdot -1) + (5 \cdot -1) - (-1 \cdot -1) + (5 \cdot 8) + (5 \cdot 5) + (-1 \cdot -4) \right|
A = \frac{1}{2} \left| -20 - 5 - 8 - 5 - 1 + 40 + 25 + 4 \right|
A = \frac{1}{2} \left| -38 + 68 \right|
A = \frac{1}{2} \left| 30 \right|
A = 39

2. **Calculate the perimeter by summing the distances between consecutive vertices:**
AB = \sqrt{(-1 - (-4))^2 + (5 - (-1))^2} = \sqrt{3^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}

BC = \sqrt{(8 - (-1))^2 + (5 - 5)^2} = \sqrt{9^2 + 0^2} = \sqrt{81} = 9

CD = \sqrt{(5 - 8)^2 + (-1 - 5)^2} = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}

DA = \sqrt{(5 - (-4))^2 + (-1 - (-1))^2} = \sqrt{9^2 + 0^2} = \sqrt{81} = 9

Adding up all the distances for the perimeter:
P = 3\sqrt{5} + 9 + 3\sqrt{5} + 9 = 6\sqrt{5} + 18 \approx 28

Thus, the area is:
A = 39

And the perimeter is:
P = 28