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

1 Answer
CW
Aug 23, 2017

Option C. 17.8 " units"

Explanation:

enter image source here
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

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