So we are given 4 points that define a polygon and we need to find its perimeter.
Those 4 points define 4 sides. The sum of their lengths gives us the perimeter we are looking for. Those lengths are given by the distances between their extremes. For example, the length of side AD is equal to the distance between A and D. For two random points (a,b) and (c,d) the distance between them is equal to:
[tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]
So let's find the length of each of the polygon's four sides. For AD we have:
[tex]\sqrt[]{(3-6)^2+(7-7)^2}=\sqrt[]{9}=3[/tex]
So its length is 3 units.
For AB we get:
[tex]\sqrt[]{(3-3)^2+(7-1)^2}=\sqrt[]{36}=6[/tex]
Then its length is 6 units.
For BC:
[tex]\sqrt[]{(3-6)^2+(1-1)^2}=\sqrt[]{9}=3[/tex]
So its length is 3 units.
And for CD we get:
[tex]\sqrt[]{(6-6)^2+(7-1)^2}=\sqrt[]{36}=6[/tex]
Then the perimeter is equal to the sum of these four lengths:
[tex]p=3+6+3+6=18[/tex]
Then the answer is 18.
