Answer:
The perimeter is the sum of the length of the sides of a certain shape. In this case, the perimeter of the polygon would be the sum of the lengths of sides AB, BC, CD, and DA.
Step-by-step explanation:
Lets start computing the length of each side of the polygon. Using points A and B as a first example, we find that the distance between them will be:
[tex]d_{AB}=\sqrt{(x_A - x_B) ^2+(y_A - y_B) ^2 }[/tex]
Where [tex](x_A , y_A )[/tex] and [tex](x_B , y_B )[/tex] are the coordinates of points A and B respectively.
From the graph we can see that point A has coordinates (5, 12), B has coordinates (9, 9), C has coordinates (12, 5), and D has coordinates (0, 0). Puting values and computing the lengths we find that:
Lenght AB:
[tex]d_{AB}=\sqrt{(x_A - x_B) ^2+(y_A - y_B) ^2}=\sqrt{(5 - 9) ^2+(12 - 9) ^2}[/tex]
[tex]d_{AB}=\sqrt{(-4) ^2+(3) ^2 } =\sqrt{16 + 9 }=\sqrt{25}[/tex]
[tex]d_{AB}=5[/tex]
Lenght BC:
[tex]d_{BC}= \sqrt{(x_B - x_C) ^2 + (y_B - y_C) ^2 } = \sqrt{(9 - 12) ^2 + (9 - 5) ^2 }[/tex]
[tex]d_{BC}=\sqrt{(-3) ^2 + (4) ^2 }=\sqrt{9 + 16 } =\sqrt{25}[/tex]
[tex]d_{BC}=5[/tex]
Lenght CD:
[tex]d_{CD}= \sqrt{(x_C - x_D) ^2 + (y_C - y_D) ^2 } = \sqrt{(12 - 0) ^2 + (5 - 0) ^2 }[/tex]
[tex]d_{CD}=\sqrt{(12) ^2 + (5) ^2 } = \sqrt{144 + 25 } = \sqrt{169}[/tex]
[tex]d_{CD}=13[/tex]
Lenght DA:
[tex]d_{DA}= \sqrt{(x_D - x_A) ^2 + (y_D - y_A) ^2 } = \sqrt{(0 - 5) ^2 + (0 - 12) ^2 }[/tex]
[tex]d_{DA}=\sqrt{(-4) ^2 + (-12) ^2 } = \sqrt{25 + 144 } = \sqrt{169}[/tex]
[tex]d_{DA}=13[/tex]
Therefor the result will be:
[tex]Perimeter = d_{AB} + d_{BC} +d_{CD} +d_{DA}= 5 + 5 + 13 + 13 = 36[/tex]
