What is the perimeter of a polygon with vertices at (-2,1) (-2,7) (1,11) (4,7) and (4,1)
Accepted Solution
A:
Answer:28 units.Step-by-step explanation:Consider vertices of the polygon are A(-2,1), B(-2,7), C(1,11), D(4,7) and E(4,1).Distance formula:[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Using distance formula we get[tex]AB=\sqrt{\left(-2-\left(-2\right)\right)^2+\left(7-1\right)^2}=6[/tex][tex]BC=\sqrt{\left(1-\left(-2\right)\right)^2+\left(11-7\right)^2}=5[/tex][tex]CD=\sqrt{\left(4-1\right)^2+\left(7-11\right)^2}=5[/tex][tex]DE=\sqrt{\left(4-4\right)^2+\left(1-7\right)^2}=6[/tex][tex]AE=\sqrt{\left(4-\left(-2\right)\right)^2+\left(1-1\right)^2}=6[/tex]The perimeter of a polygon is[tex]Perimeter=AB+BC+CD+DE+AE[/tex][tex]Perimeter=6+5+5+6+6[/tex][tex]Perimeter=28[/tex]Therefore, the perimeter of the polygon is 28 units.