Answer: The correct option is A. The perimeter of the polygon is 15.2 units.
Explanation:
The perimeter of a shape is the sum of its all sides.
Let the vertices of the polygon be ABCDE.
[tex]\text{perimeter}=AB+BC+CD+DE+AD[/tex]
Use distance formula to find the length of sides.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(3-1)^2+(-3+2)^2}=\sqrt{4+1}=\sqrt{5}[/tex]
[tex]BC=\sqrt{(5-3)^2+(-1+3)^2}=\sqrt{4+4}=\sqrt{8}[/tex]
[tex]CD=\sqrt{(4-5)^2+(2+1)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
[tex]DE=\sqrt{(1-4)^2+(2-2)^2}=\sqrt{9+0}=3[/tex]
[tex]AE=\sqrt{(1-1)^2+(-2-2)^2}=\sqrt{0+16}=4[/tex]
So, the length of sides are [tex]\sqrt{5},\sqrt{10},\sqrt{8}, 3,4[/tex]
[tex]\text{perimeter}=\sqrt{5}+ \sqrt{10}+ \sqrt{8}+ 3+4[/tex]
[tex]\text{perimeter}=2.23+3.16+2.83+7[/tex]
[tex]\text{perimeter}=15.22[/tex]
When we Approx 15.22 to nearest tenth, we get 15.2.
Therefore, A is the correct option.
