Answer:
12.32 units
Step-by-step explanation:
Use the distance formula to find the lengths between two points:
[tex]d=\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
the distance between (-2, -1) and (-5,-1) is
[tex]\sqrt{(-2-(-5))^2+(-1-(-1))^2}[/tex]
=[tex]\sqrt{3^2+0^2}[/tex]
=[tex]\sqrt{9}[/tex]
=3
the distance between (-2, -1) and (-3, -4) is
[tex]\sqrt{(-2-(-3))^2+(-1-(-4))^2}[/tex]
=[tex]\sqrt{1^2+3^2}[/tex]
=[tex]\sqrt{10}[/tex]
≈3.16
the distance between (-6, -4) and (-3, -4) is
[tex]\sqrt{(-6-(-3))^2+(-4-(-4))^2}[/tex]
=[tex]\sqrt{(-3)^2+0^2}[/tex]
=[tex]\sqrt{9}[/tex]
=3
the distance between (-6, -4) and (-5, -1) is
[tex]\sqrt{(-6-(-5))^2+(-4-(-1)^2}[/tex]
=[tex]\sqrt{(-1)^2+3^2}[/tex]
=[tex]\sqrt{10}[/tex]
≈3.16
Now, add all the sides:
3+3.16+3+3.16=12.32 units
Note: A property of a parallelogram is that it has two pairs of congruent sides, so for this problem, you could solve for 2 different sides, double them, then add and you will get the same thing.
