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?


Round each length to the nearest tenth of a unit.

Enter your answer as a decimal.

Answer 1

let is find the absolute value of all x components...

|-5--1|+|2--1|+|2-2|+|-3-2|+|-5--3|

4+3+0+5+2=14

So the total x displacement is 14 units

now find the absolute value of all y components...

|1-3|+|3-3|+|-2-3|+|-1--2|+|-1-1|

2+0+5+1+2=10

So the total y displacement is 10 units...

So the perimeter is the hypotenuse of these two displacements...

p=√(14^2+10^2)

p=√296

p≈17.2 units