Answer:
32.2 units
Step-by-step explanation:
The perimeter of the figure = AB + BC + CD + DE + EF + FA
AB = |5 - 11| = 6 units
BC = |-8 - 0| = 8 units
[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] C(11, 0) = (x_1, y_1) [/tex]
[tex] D(6, -3) = (x_2, y_2) [/tex]
[tex] CD = \sqrt{(6 - 11)^2 + (-3 - 0)^2} [/tex]
[tex] CD = \sqrt{(-5)^2 + (-3)^2} [/tex]
[tex] CD = \sqrt{25 + 9} = \sqrt{34} [/tex]
[tex] CD = 5.8 units [/tex] (nearest tenth)
DE = |6 - 4| = 2 units
[tex] EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] E(4, -3) = (x_1, y_1) [/tex]
[tex] F(0, -6) = (x_2, y_2) [/tex]
[tex] EF = \sqrt{(0 - 4)^2 + (-6 -(-3))^2} [/tex]
[tex] EF = \sqrt{(-4)^2 + (-3)^2} [/tex]
[tex] EF = \sqrt{16 + 9} = \sqrt{25} [/tex]
[tex] EF = 5 units [/tex]
[tex] FA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] F(0, -6) = (x_1, y_1) [/tex]
[tex] A(5, -8) = (x_2, y_2) [/tex]
[tex] FA = \sqrt{(5 - 0)^2 + (-8 -(-6))^2} [/tex]
[tex] FA = \sqrt{(5)^2 + (-2)^2} [/tex]
[tex] FA = \sqrt{25 + 4} = \sqrt{29} [/tex]
[tex] FA = 5.4 units [/tex] (nearest tenth)
Perimeter = 6 + 8 + 5.8 + 2 + 5 + 5.4
= 32.2 units
