Given:
The coordinates are,
[tex]\begin{gathered} A(-3,5) \\ B(2,6) \\ C(0,2) \\ D(-5,1) \end{gathered}[/tex]
To find:
The perimeter
Explanation:
We know that,
The perimeter is the sum of all sides.
So, let us find the distance between the adjacent coordinates.
The distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance AB is,
[tex]\begin{gathered} AB=\sqrt{(2+3)^2+(6-5)^2} \\ =\sqrt{5^2+1^2} \\ =\sqrt{26\text{ }}units \end{gathered}[/tex]
The distance BC is,
[tex]\begin{gathered} BC=\sqrt{(0-2)^2+(2-6)^2} \\ =\sqrt{2^2+4^2} \\ =\sqrt{20\text{ }}units \end{gathered}[/tex]
The distance CD is,
[tex]\begin{gathered} CD=\sqrt{(-5-0)^2+(1-2)^2} \\ =\sqrt{5^2+1^2} \\ =\sqrt{26\text{ }}units \end{gathered}[/tex]
The distance DA is,
[tex]\begin{gathered} DA=\sqrt{(-3+5)^2+(5-1)^2} \\ =\sqrt{2^2+4^2} \\ =\sqrt{20\text{ }}units \end{gathered}[/tex]
Therefore, the perimeter is
[tex]\begin{gathered} P=AB+BC+CD+DA \\ =\sqrt{26}+\sqrt{20}+\sqrt{26}+\sqrt{20} \\ =2\sqrt{26}+2\sqrt{20} \\ P=19.14 \\ P\approx19.1units \end{gathered}[/tex]
Thus, the perimeter of the given shape is 19.1 units.
Final answer:
The perimeter of the given shape is 19.1 units.
