Answer:
12.32 units
Explanation:
To find the perimeter of a parallelogram, we need to sum the lengths of all four sides.
Let's calculate the lengths of the sides using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the lengths of the four sides of the parallelogram:
Side 1:
(x1, y1) = (-5, -1)
(x2, y2) = (-2, -1)
d1 = √((-2 - (-5))^2 + (-1 - (-1))^2)
= √(3^2 + 0^2)
= √(9)
= 3
Side 2:
(x1, y1) = (-2, -1)
(x2, y2) = (-3, -4)
d2 = √((-3 - (-2))^2 + (-4 - (-1))^2)
= √((-1)^2 + (-3)^2)
= √(1 + 9)
= √(10)
≈ 3.16
Side 3:
(x1, y1) = (-3, -4)
(x2, y2) = (-6, -4)
d3 = √((-6 - (-3))^2 + (-4 - (-4))^2)
= √((-3)^2 + 0^2)
= √(9)
= 3
Side 4:
(x1, y1) = (-6, -4)
(x2, y2) = (-5, -1)
d4 = √((-5 - (-6))^2 + (-1 - (-4))^2)
= √(1^2 + 3^2)
= √(1 + 9)
= √(10)
≈ 3.16
Now, let's calculate the perimeter by adding the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
= 3 + 3.16 + 3 + 3.16
≈ 12.32
Therefore, the approximate perimeter of the parallelogram is 12.32.