Answer:
Its perimeter is 23 units
Step-by-step explanation:
The perimeter of any figure is the sum of the lengths of its outline sides
The rule of the distance between two points is:
In the given figure ABCD:
Its perimeter = AB + BC + CD + DE + EA
→ Find the length of each side using the rule above
A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)
→ Substitute them in the rule above to find the lengths of its sides
![AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28-1--4%29%5E%7B2%7D%2B%282--2%29%5E%7B2%7D%7D%3D%5Csqrt%7B%28-1%2B4%29%5E%7B2%7D%2B%282%2B2%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D%3D%5Csqrt%7B9%2B16%7D%3D%5Csqrt%7B25%7D)
∴ AB = 5
![BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%282--1%29%5E%7B2%7D%2B%282-2%29%5E%7B2%7D%7D%3D%5Csqrt%7B%282%2B1%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B0%7D%3D%5Csqrt%7B9%2B0%7D%3D%5Csqrt%7B9%7D)
∴ BC = 3
![CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%285-2%29%5E%7B2%7D%2B%28-1-2%29%5E%7B2%7D%7D%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B9%2B9%7D%3D%5Csqrt%7B18%7D)
∴ CD = ![\sqrt{18}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D)
![DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B%282-5%29%5E%7B2%7D%2B%28-4--1%29%5E%7B2%7D%7D%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%28-4%2B1%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%7D%3D%5Csqrt%7B9%2B9%7D%3D%5Csqrt%7B18%7D)
∴ DE = ![\sqrt{18}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D)
![EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}](https://tex.z-dn.net/?f=EA%3D%5Csqrt%7B%28-4-2%29%5E%7B2%7D%2B%28-2--4%29%5E%7B2%7D%7D%3D%5Csqrt%7B%28-6%29%5E%7B2%7D%2B%28-2%2B4%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%28-6%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D%3D%5Csqrt%7B36%2B4%7D%3D%5Csqrt%7B40%7D)
∴ EA = ![\sqrt{40}](https://tex.z-dn.net/?f=%5Csqrt%7B40%7D)
→ Add them to find the perimeter of the figure ABCDE
∴ Its perimeter = 5 + 3 +
+
+
≅ 22.8098
→ Round it to the whole number
∴ Its perimeter = 23 units