Answer:
The perimeter of a quadrilateral will be equal to the addition of the length of each side of the quadrilateral.
Here we only have the vertices of the quadrilateral, and to calculate the length of the sides, first we need to plot the points in a graph and see which pairs make the quadrilateral.
You can see the image below, where i did a rough sketch of the problem.
in the image, you can see that the sides of this rectangle are the ones formed by the pairs:
(-4,3) and (-2, 8)
(-2, 8) and (2, 5)
(2,5 ) and (1, -7)
(1, - 7) and (-4, 3)
Now let's calculate the length of each side.
Remember that when we have two points (a, b) and (c, d) the distance is:
D = √( (a - c)^2 + (b - d)^2)
Now we need to calculate four distances:
(-4,3) and (-2, 8)
D1 = √( (-4 + 2)^2 + (3 - 8)^2) = 5.39
(-2, 8) and (2, 5)
D2 = √( (-2 - 2)^2 + (8 - 5)^2) = 5
(2,5 ) and (1, -7)
D3 = √( (2 - 1)^2 + (5 + 7)^2) = 12.04
(1, - 7) and (-4, 3)
D4 = √( (1 +4)^2 + (-7 -3)^2) = 11.18
Now we add those four distances to get the perimeter:
P = 5.39 + 5 + 12.04 + 11.18 = 33.61
And we want to round it to the next whole number, because the first digit after the decimal point is larger than 5, we round up, and get:
p = 37