46.5k views
0 votes
What is the perimeter of a polygon with vertices at (−1, 3), ​(−1, 6)​, (2, 10), ​(5, 6)​​, and ​​ ​(5, 3)​?

1 Answer

4 votes

To find the perimeter of the polygon with the given vertices, you need to calculate the sum of the lengths of its sides. The polygon has five sides:

Side 1: From (-1, 3) to (-1, 6)

Length = 6 - 3 = 3 units

Side 2: From (-1, 6) to (2, 10)

Length = √((2 - (-1))^2 + (10 - 6)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 units

Side 3: From (2, 10) to (5, 6)

Length = √((5 - 2)^2 + (6 - 10)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5 units

Side 4: From (5, 6) to (5, 3)

Length = 6 - 3 = 3 units

Side 5: From (5, 3) to (-1, 3)

Length = √((-1 - 5)^2 + (3 - 3)^2) = √((-6)^2 + 0) = √(36) = 6 units

Now, sum the lengths of all the sides to find the perimeter:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4 + Side 5

Perimeter = 3 + 5 + 5 + 3 + 6

Perimeter = 22 units

So, the perimeter of the polygon is 22 units.

User Kazuya  Gosho
by
7.5k points