Question

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 7) ​, (1, 11) , ​ (4, 7) ​ ​, and ​​ ​ (4, 1) ​ ?

Answer 1

Each edge is given by the distance formula, which is the Pythagorean Theorem. When one of the coordinates is the same, we can shortcut that.

A(−2, 1) , B(−2, 7)​, C(1, 11), D(4, 7)​, E(4, 1)

$AB=7-1=6$

$BC=\sqrt{(1 - -2)^2 + (11-7)^2}=5$

$CD=\sqrt{(4 - 1 )^2 + (11-7)^2}=5$

$DE=7-1=6$

$EA= 4 - -2 = 6$

$\textrm{perimeter} = 6+5+5+6+6=28$

Answer: 28