Question

what is the perimeter of a polygon with vertices at (-1, 3), (-1, 6), (2, 10), (5, 6), and (5, 3)? enter your answer in the box. do not round any side lengths.

Explanation:

Step1: Recall distance formula

The distance formula 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: Calculate side - 1 length

For points $(-1,3)$ and $(-1,6)$: $x_1=-1,y_1 = 3,x_2=-1,y_2 = 6$. Then $d_1=\sqrt{(-1+1)^2+(6 - 3)^2}=\sqrt{0 + 9}=3$.

Step3: Calculate side - 2 length

For points $(-1,6)$ and $(2,10)$: $x_1=-1,y_1 = 6,x_2=2,y_2 = 10$. Then $d_2=\sqrt{(2 + 1)^2+(10 - 6)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step4: Calculate side - 3 length

For points $(2,10)$ and $(5,6)$: $x_1=2,y_1 = 10,x_2=5,y_2 = 6$. Then $d_3=\sqrt{(5 - 2)^2+(6 - 10)^2}=\sqrt{9+16}=\sqrt{25}=5$.

Step5: Calculate side - 4 length

For points $(5,6)$ and $(5,3)$: $x_1=5,y_1 = 6,x_2=5,y_2 = 3$. Then $d_4=\sqrt{(5 - 5)^2+(3 - 6)^2}=\sqrt{0 + 9}=3$.

Step6: Calculate side - 5 length

For points $(5,3)$ and $(-1,3)$: $x_1=5,y_1 = 3,x_2=-1,y_2 = 3$. Then $d_5=\sqrt{(-1 - 5)^2+(3 - 3)^2}=\sqrt{36+0}=6$.

Step7: Calculate perimeter

$P=d_1 + d_2+d_3+d_4+d_5=3 + 5+5+3+6=22$.

Answer:

22