Question

A parallelogram has vertices at (-5, -1), (-2, -1), (-3, -4), and (-6, -4). What is the approximate perimeter of the parallelogram? Round your answers to the nearest hundredth.

Answer 1

Hello,

A=(-5,-1)
B=(-2,-1)
C=(-3,-4)
|AB|²=(-5+2)²+(-1+1)²=9==>|AB|=3
|BC|²=(-3+2)²+(-4+1)²=1+9=10 ==>|BC|=√10

Perimeter=2*3+2*√10=6+2√10≈12.32

Answer 2

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:

`AB=√((-1+1)^2+(-2+5)^2)=√(0+9)=\sqrt9=3~\textup{units},\\\\BC=√((-4+1)^2+(-3+2)^2)=√(9+1)=√(10)=3.16~\textup{units}.`

Since the opposite sides of a parallelogram are congruent, so the perimeter of parallelogram ABCD will be

`P=2(AB+BC)=2(3+3.16)=2*6.16=12.32~\textup{units}.`

Thus, the required perimeter of the given parallelogram is 12.32 units.