Question

Help!What is the answer to this question?​

Answer 1

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:

• $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

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

$AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}$

∴ AB = 5

$BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}$

∴ BC = 3

$CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}$

∴ CD = $\sqrt{18}$

$DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}$

∴ DE = $\sqrt{18}$

$EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}$

∴ EA = $\sqrt{40}$

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + $\sqrt{18}$ + $\sqrt{18}$ +$\sqrt{40}$ ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units