Question

The coordinates of the vertices of a polygon are (0,3), (2,3) (2,0), (1,-4) and (-2,-1). What is the perimeter of the polygon to the nearest tenth of a unit?

A. 15.8 units

B. 16.9 units

C. 17.8 units

D. 18.6 units

Answer 1

Option C. `17.8 " units"`

Explanation:

As shown in th figure, `ABCDE` is the polygon.
perimeter of the polygon `p=AB+BC+CD+DE+EA`
As `AB` is a horizontal line, `=> AB=|2-0|=2`
As `BC` is a vertical line, `=> BC=|0-3|=3`
Use the distance formula to find `CD,DE and EA`
`CD=sqrt((1-2)^2+(-4-0)^2)=sqrt(1+16)=sqrt17`
`DE=sqrt((-2-1)^2+(-1-(-4))^2)=sqrt(9+9)=sqrt18`
`EA=sqrt((0-(-2))^2+(3-(-1))^2)=sqrt(4+16)=sqrt20`

`=>` perimeter `p=2+3+sqrt17+sqrt18+sqrt20~~17.8` units