Question

The coordinates of the vertices of a polygon are (−2,1), (−3,3), (−1,5), (2,4), and (2,1).

What is the perimeter of the polygon to the nearest tenth of a unit?

15.2 units

15.9 units

16. 5 units

18.8 units

Answer 1

15.2 units

Step-by-step explanation:

Answer 2

Answer: The correct option is A. The perimeter of the polygon is 15.2 units.

Step-by-step explanation:

The perimeter of a shape is the sum of its all sides.

Let the vertices of the polygon be ABCDE.

`\text{perimeter}=AB+BC+CD+DE+AD`

Use distance formula to find the length of sides.

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

`AB=√((3-1)^2+(-3+2)^2)=√(4+1)=√(5)`

`BC=√((5-3)^2+(-1+3)^2)=√(4+4)=√(8)`

`CD=√((4-5)^2+(2+1)^2)=√(1+9)=√(10)`

`DE=√((1-4)^2+(2-2)^2)=√(9+0)=3`

`AE=√((1-1)^2+(-2-2)^2)=√(0+16)=4`

So, the length of sides are
`√(5),√(10),√(8), 3,4`

`\text{perimeter}=√(5)+ √(10)+ √(8)+ 3+4`

`\text{perimeter}=2.23+3.16+2.83+7`

`\text{perimeter}=15.22`

When we Approx 15.22 to nearest tenth, we get 15.2.

Therefore, A is the correct option.