Question

The 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? Round each length to the nearest tenth of a unit.

Answer 1

Given the coordinates of the vertices of a polygon  (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0,−2), the perimeter of the polygon is 18.  It is the sum of the length of five sides.

Answer 2

Total perimeter of the pentagon can be calculated by adding the length of the sides.
Perimeter = d1+d2+d3+d4+d5
Distances between coordinate is computed using the distance formula.
d 1= sqrt(-2+2)^2+(3+2)^2
d1 =5
d2 = sqrt(2+2)^2+(4-3)^2
d2= sqrt17=4.1
d3= sqrt(3-2)^2+(1-4)^2
d3=sqrt10=3.2
d4=sqrt(0-3)^2+(-2-1)^2
d4=sqrt18=4.2
d5=sqrt(-2-0)^2+(-2+2)^2
d5= 2
Perimeter of the pentagon = 5+4.1+3.2+4.2+2
= 18.5