Question

perimeter
perimeter
the perimeter of a polygon is the distance around the polygon and it can be found by adding all its side - lengths together.
you can calculate unknown side - lengths of a polygon on a coordinate plane by using the distance formula, $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, or pythagorean theorem, $a^{2}+b^{2}=c^{2}$.
lets try:
find the perimeter of efgh. round to the nearest tenth if necessary.
e(-2, 6), f(4, 3), g(4, -1), h(-4, -2)

1. graph quadrilateral efgh.
2. find the length of ef.

d = $sqrt{(-2 - 4)^{2}+(6 - 3)^{2}}=sqrt{( - 6)^{2}+3^{2}}=sqrt{36 + 9}$

1. find the length of fg.
2. find the length of gh.
3. find the length of eh.
4. add all 4 side lengths to find the perimeter of efgh.

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find length of EF

For $E(-2,6)$ and $F(4,3)$, $x_1=-2,y_1 = 6,x_2=4,y_2 = 3$. Then $d_{EF}=\sqrt{(4 - (-2))^2+(3 - 6)^2}=\sqrt{(6)^2+(-3)^2}=\sqrt{36 + 9}=\sqrt{45}\approx6.7$.

Step3: Find length of FG

For $F(4,3)$ and $G(4,-1)$, $x_1 = 4,y_1=3,x_2 = 4,y_2=-1$. Then $d_{FG}=\sqrt{(4 - 4)^2+(-1 - 3)^2}=\sqrt{0+( - 4)^2}=\sqrt{16}=4$.

Step4: Find length of GH

For $G(4,-1)$ and $H(-4,-2)$, $x_1 = 4,y_1=-1,x_2=-4,y_2=-2$. Then $d_{GH}=\sqrt{(-4 - 4)^2+(-2+1)^2}=\sqrt{(-8)^2+(-1)^2}=\sqrt{64 + 1}=\sqrt{65}\approx8.1$.

Step5: Find length of EH

For $E(-2,6)$ and $H(-4,-2)$, $x_1=-2,y_1 = 6,x_2=-4,y_2=-2$. Then $d_{EH}=\sqrt{(-4 + 2)^2+(-2 - 6)^2}=\sqrt{(-2)^2+(-8)^2}=\sqrt{4 + 64}=\sqrt{68}\approx8.2$.

Step6: Calculate perimeter

$P=d_{EF}+d_{FG}+d_{GH}+d_{EH}\approx6.7 + 4+8.1+8.2=27.0$.

Answer:

$27.0$