Suppose a parallelogram is drawn on a coordinate plane. Using vertices with the coordinates (2,1)
, (2,3)
, (4,4)
, and (4,2)
, compute the perimeter. Round your answer to the nearest tenth.(1 point)
The perimeter is approximately units.
To find the perimeter of a parallelogram, we need to find the lengths of all four sides and then add them up.
Using the distance formula, we can find the lengths of the sides:
Side 1: length = sqrt((4-2)^2 + (4-3)^2) = sqrt(2^2 + 1^2) = sqrt(4+1) = sqrt(5) ≈ 2.24
Side 2: length = sqrt((4-2)^2 + (2-1)^2) = sqrt(2^2 + 1^2) = sqrt(4+1) = sqrt(5) ≈ 2.24
Side 3: length = sqrt((4-4)^2 + (2-3)^2) = sqrt(0^2 + (-1)^2) = sqrt(0+1) = sqrt(1) = 1
Side 4: length = sqrt((2-2)^2 + (3-1)^2) = sqrt(0^2 + 2^2) = sqrt(0+4) = sqrt(4) = 2
Now, we can add up all the lengths to find the perimeter:
Perimeter ≈ 2.24 + 2.24 + 1 + 2 = 7.48
Rounded to the nearest tenth, the perimeter is approximately 7.5 units.