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.
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.