Question

30 POINTS! ANSWER ASAP PLEASE!!! WILL THANK ACCOUNT AND ALL ANSWERS!!

The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).



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



15.3 units
16.9 units
17.5 units
17.9 units

Answer 1

16.9 units

Explanation:

Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...

14.87 + 2 = 16.87 ≈ 16.9 . . . units

_____

The distance formula can be used to find the lengths of individual segments. It tells you ...

d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

If the segments are labeled A, B, C, D, E in order, the distances are ...

AB = √(5²+1²) = √26 ≈ 5.099

BC = √(1²+3²) = √10 ≈ 3.162

CD = Δx = 3

DE = √(3²+2²) = √13 ≈ 3.606

EA = Δy = 2

Then the perimeter is ...

P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

P ≈ 16.9