Applying the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 32 units.
Recall:
- Perimeter of a polygon is the sum of all its sides.
- Distance between two vertices having coordinates can be calculated using the distance formula given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]
Assume the vertices of the polygon are named as:
- A(3, 2)
- B(3, 9)
- C(7, 12)
- D(11, 9)
- E(11, 2)
Perimeter of the polygon = AB + BC + CD + DE + AE
- Find the distance between A(3, 2) and B(3, 9) using the distance formula:
[tex]AB = \sqrt{(9 - 2)^2 + (3 - 3)^2}\\\\AB = \sqrt{7^2 + 0^2} \\\\AB = \sqrt{49} \\\\\mathbf{AB = 7}[/tex]
- Find the distance between B(3, 9) and C(7, 12) using the distance formula:
[tex]BC = \sqrt{(12 - 9)^2 + (7 - 3)^2}\\\\BC = \sqrt{3^2 + 4^2} \\\\BC = \sqrt{25} \\\\\mathbf{BC = 5}[/tex]
- Find the distance between C(7, 12) and D(11, 9) using the distance formula:
[tex]CD = \sqrt{(9 - 12)^2 + (11 - 7)^2}\\\\CD = \sqrt{-3^2 + 4^2} \\\\CD = \sqrt{25} \\\\\mathbf{CD = 5}[/tex]
- Find the distance between D(11, 9) and E(11, 2) using the distance formula:
[tex]DE = \sqrt{(2 - 9)^2 + (11 - 11)^2}\\\\DE = \sqrt{-7^2 + 0^2} \\\\DE = \sqrt{49} \\\\\mathbf{DE = 7}[/tex]
- Find the distance between A(3, 2) and E(11, 2) using the distance formula:
[tex]AE = \sqrt{(2 - 2)^2 + (11 - 3)^2}\\\\AE = \sqrt{0^2 + 8^2} \\\\AE = \sqrt{64} \\\\\mathbf{AE = 8}[/tex]
Perimeter of the polygon = 7 + 5 + 5 + 7 + 8 = 32 units.
In summary, applying the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 32 units.
Learn more here:
https://brainly.com/question/9920662
