Question

Find the perimeter of the polygon in kilometers (-5 -6), (2, -6) , (-5, 6) ,( 6, 6 )(2, 1) (6, 1)

Answers

GPT 3.5
To find the perimeter of the polygon, we need to add up the total distance of all the sides.

First, let's calculate the distance between each pair of points:

1. (-5, -6) to (2, -6):
Distance = |2 - (-5)| = 7 km

2. (-5, -6) to (-5, 6):
Distance = |6 - (-6)| = 12 km

3. (-5, 6) to (6, 6):
Distance = |6 - (-5)| = 11 km

4. (6, 6) to (2, 1):
Distance = √[(2 - 6)^2 + (1 - 6)^2] = √[(-4)^2 + (-5)^2] = √(16 + 25) = √41 km

5. (2, 1) to (6, 1):
Distance = |6 - 2| = 4 km

6. (6, 1) to (-5, -6):
Distance = √[(-5 - 6)^2 + (-6 - 1)^2] = √[(-11)^2 + (-7)^2] = √(121 + 49) = √170 km

Now, add all the distances together to find the perimeter:
7 + 12 + 11 + √41 + 4 + √170 = 34 + √41 + √170 km

Therefore, the perimeter of the polygon is 34 + √41 + √170 km.