Question

find the perimeter of polygon abcde. write your answer as a whole number or a decimal rounded to the nearest tenth.

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 AB

For points $A(-2,3)$ and $B(2,2)$, $d_{AB}=\sqrt{(2 + 2)^2+(2 - 3)^2}=\sqrt{16 + 1}=\sqrt{17}\approx 4.1$.

Step3: Find length of BC

For points $B(2,2)$ and $C(4, - 1)$, $d_{BC}=\sqrt{(4 - 2)^2+(-1 - 2)^2}=\sqrt{4 + 9}=\sqrt{13}\approx 3.6$.

Step4: Find length of CD

For points $C(4,-1)$ and $D(0,-3)$, $d_{CD}=\sqrt{(0 - 4)^2+(-3 + 1)^2}=\sqrt{16+4}=\sqrt{20} = 2\sqrt{5}\approx4.5$.

Step5: Find length of DE

For points $D(0,-3)$ and $E(-3,-2)$, $d_{DE}=\sqrt{(-3 - 0)^2+(-2 + 3)^2}=\sqrt{9 + 1}=\sqrt{10}\approx 3.2$.

Step6: Find length of EA

For points $E(-3,-2)$ and $A(-2,3)$, $d_{EA}=\sqrt{(-2+3)^2+(3 + 2)^2}=\sqrt{1 + 25}=\sqrt{26}\approx 5.1$.

Step7: Calculate perimeter

$P=d_{AB}+d_{BC}+d_{CD}+d_{DE}+d_{EA}\approx4.1+3.6 + 4.5+3.2+5.1=20.5$.

Answer:

$20.5$