Question

The coordinates of the vertices of a polygon are (−5, 1), (−1, 3), (2, 3), (2, −2), and (−3, −1).

What is the perimeter of the polygon?



Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
units

Answer 1

Compute the distances between successive vertices and sum them.

AB: between (−5,1) and (−1,3): sqrt(4^2+2^2)=sqrt(20)≈4.4721
BC: between (−1,3) and (2,3): 3
CD: between (2,3) and (2,−2): 5
DE: between (2,−2) and (−3,−1): sqrt(5^2+1^2)=sqrt(26)≈5.0990
EA: between (−3,−1) and (−5,1): sqrt(2^2+2^2)=sqrt(8)≈2.8284

Perimeter ≈ 4.4721+3+5+5.0990+2.8284 = 20.3996 ≈ 20.4 units.