Answer:
26.13 units.
Step-by-step explanation:
We are asked to find the perimeter of the given figure.
First of all we will find the length of each line segment using distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\text{Distance between Q and R}=\sqrt{(2-4)^2+(0-5)^2}[/tex]
[tex]\text{Distance between Q and R}=\sqrt{(-2)^2+(-5)^2}[/tex]
[tex]\text{Distance between Q and R}=\sqrt{4+25}[/tex]
[tex]\text{Distance between Q and R}=\sqrt{29}[/tex]
[tex]\text{Distance between R and S}=\sqrt{(4-8)^2+(5-7)^2}[/tex]
[tex]\text{Distance between R and S}=\sqrt{(-4)^2+(-2)^2}[/tex]
[tex]\text{Distance between R and S}=\sqrt{16+4}[/tex]
[tex]\text{Distance between R and S}=\sqrt{20}[/tex]
[tex]\text{Distance between S and T}=\sqrt{(8-6)^2+(7-4)^2}[/tex]
[tex]\text{Distance between S and T}=\sqrt{(2)^2+(3)^2}[/tex]
[tex]\text{Distance between S and T}=\sqrt{4+9}[/tex]
[tex]\text{Distance between S and T}=\sqrt{13}[/tex]
[tex]\text{Distance between T and U}=\sqrt{(6-10)^2+(4-3)^2}[/tex]
[tex]\text{Distance between T and U}=\sqrt{(-4)^2+(1)^2}[/tex]
[tex]\text{Distance between T and U}=\sqrt{16+1}[/tex]
[tex]\text{Distance between T and U}=\sqrt{17}[/tex]
[tex]\text{Distance between U and Q}=\sqrt{(10-2)^2+(3-0)^2}[/tex]
[tex]\text{Distance between U and Q}=\sqrt{(8)^2+(3)^2}[/tex]
[tex]\text{Distance between U and Q}=\sqrt{64+9}[/tex]
[tex]\text{Distance between U and Q}=\sqrt{73}[/tex]
Let us add all the lengths to find the perimeter of our given figure.
[tex]\text{Perimeter}=\sqrt{29}+\sqrt{20}+\sqrt{13}+\sqrt{17}+\sqrt{73}[/tex]
[tex]\text{Perimeter}=26.1299614085332644\approx 26.13[/tex]
Therefore, the perimeter of our given image will be 26.13 units.
