Answer: The required perimeter of the given parallelogram is 12.32 units.
Step-by-step explanation: Given that the co-ordinates of the vertices of a parallelogram are (-5, -1), (-2, -1), (-3, -4), and (-6, -4).
We are to find the approximate perimeter of the parallelogram.
Let the vertices of the given parallelogram be doted by A(-5, -1), B(-2, -1), C(-3, -4), and D(-6, -4).
So, the lengths of two adjacent sides AB and BC are calculated using distance formula, as follows:
[tex]AB=\sqrt{(-1+1)^2+(-2+5)^2}=\sqrt{0+9}=\sqrt9=3~\textup{units},\\\\BC=\sqrt{(-4+1)^2+(-3+2)^2}=\sqrt{9+1}=\sqrt{10}=3.16~\textup{units}.[/tex]
Since the opposite sides of a parallelogram are congruent, so the perimeter of parallelogram ABCD will be
[tex]P=2(AB+BC)=2(3+3.16)=2\times6.16=12.32~\textup{units}.[/tex]
Thus, the required perimeter of the given parallelogram is 12.32 units.
