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.

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.

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           

Recall that area of the triangle is 1/2*(base)*(height)1/2*(13)*(17) = 110.5the answer is 110.5