Question

He coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .

What is the perimeter of the polygon?



Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.

Answer 1

The perimeter of the polygon is 18.64 units.

Step-by-step explanation:

To find the perimeter of a polygon, we need to sum the lengths of all its sides. Let's calculate the distance between each consecutive pair of vertices and add them up.

The distance between (-2, -2) and (-2, 3) is 5 units.

The distance between (-2, 3) and (2, 4) is 4.24 units (rounded to the nearest tenth).

The distance between (2, 4) and (3, 1) is 3.16 units (rounded to the nearest tenth).

The distance between (3, 1) and (0, -2) is 4.24 units (rounded to the nearest tenth).

The distance between (0, -2) and (-2, -2) is 2 units.

Adding up these distances, the perimeter of the polygon is 5 + 4.24 + 3.16 + 4.24 + 2 = 18.64 units (rounded to the nearest tenth).

Answer 2

Answer: The perimeter is 17.52

Step-by-step explanation:

1. You can plot the points, as you can see in the graph attached.

2. As you can see in the graph, the points are:

`A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)`

And the lenghts AB and EA are:

`AB=5`

`EA=2`

3. To find the other lenghts, you can apply the formula for calculate the distance between two points:

`distance=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

4. Thefore, you have:

`BC=\sqrt{(2-(-2))^(2)+(4-3)^(2)}=4.12\\CD=\sqrt{(2-3)^(2)+(4-1)^(2)}=3.16\\DE=\sqrt{(3-0)^(2)+(1-(-2))^(2)}=4.24`

5. The perimeter is:

`P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52`