Question

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

Enter your answer in the box. Do not round any side lengths.​

____ units

Answer 1

First we need the distances of the sides of the polygon, because perimeter = sum of all sides.

`d = \sqrt{{(y2 - y1)}^(2) + {(x2 - x1)}^(2) }`

`d1 = \sqrt{{(1 - 4)}^(2) + {( - 2 - - 2)}^(2) } \\ = \sqrt{{(- 3)}^(2) + {(0)}^(2) } = √(9) \: = 3`

`d2 = \sqrt{{(4 - 7)}^(2) + {( - 2 - 2)}^(2) } \\ = \sqrt{{(- 3)}^(2) + {( -4)}^(2) } = √(9 + 16) \\ = √(25) \: = 5`

`d3 \: = \sqrt{{(7 - 4)}^(2) + {(2 - 6)}^(2) } \\ = \sqrt{{(3)}^(2) + {( - 4)}^(2) } = √(9 + 16) \\ = √(25) \: = 5`

`d4 = \sqrt{{(4 - 1)}^(2) + {(6 - 6)}^(2) } \\ = \sqrt{ {(3)}^(2) + {(0)}^(2) } = √(9) \: = 3`

`d5 = \sqrt{{(1 - 1)}^(2) + {(-2 - 6)}^(2) } \\ = \sqrt{ {(0)}^(2) + {( - 4)}^(2)} = √(16) \: = 4`
Now, we add all sides for the perimeter:
p = d1 + d2 + d3 + d4 + d5
p = 3+5+5+3+4 = 20 units

Answer 2

The other answer was using the formula correctly through most of the problem, but made a mistake when finding the last distance (#5). The person took away (-2-6 = - 4), which is incorrect. The correct answer is -8 because your adding two negatives. So, the correct answer for the whole problem is 24 units.

Good job to the person who answer they did the whole math problem - just made a little mistake at the end.