Question

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

Enter your answer in the box. Do not round any side lengths.

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=√((1 - -2)^2 + (11-7)^2)=5`

`CD=√((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