Answer:
The perimeter of the polygon is 22.
Step-by-step explanation:
Let [tex]A(x,y) =(-3,1)[/tex], [tex]B(x,y) = (5,1)[/tex], [tex]C(x,y) = (-3, 4)[/tex] and [tex]D(x,y) =(5,4)[/tex] the vertices of the polygon. From Geometry we know that number of side of polygons equals their number of vertices, then we notice that a quadrilateral is here. In addition, we conclude that such quadrilateral is a rectangle:
1) [tex]x_{A} = x_{C}[/tex]
2) [tex]x_{B} = x_{D}[/tex]
3) [tex]y_{A} = y_{B}[/tex]
4) [tex]y_{C} = y_{D}[/tex]
Hence, we find that [tex]AB = CD[/tex] and [tex]AC = BD[/tex].
Then we find all lengths of the rectangle by Pythagorean Theorem:
[tex]AB = \sqrt{[5-(-3)]^{2}+(1-1)^{2}}[/tex]
[tex]AB =8[/tex]
[tex]AC = \sqrt{[(-3)-(-3)]^{2}+(4-1)^{2}}[/tex]
[tex]AC = 3[/tex]
By Geometry, we conclude that [tex]CD = 8[/tex] and [tex]BD = 3[/tex].
Then, the perimeter of the rectangle ([tex]p[/tex]), dimensionless, is defined by the following formula:
[tex]p = 2\cdot (s+l)[/tex] (Eq. 1)
Where:
[tex]s[/tex] - Shortest length, dimensionless.
[tex]l[/tex] - Longest length, dimensionless.
If we know that [tex]s = 3[/tex] and [tex]l = 8[/tex], then the perimeter of the rectangle is:
[tex]p = 2\cdot (3+8)[/tex]
[tex]p = 22[/tex]
The perimeter of the polygon is 22.
