Question

Find the perimeter of the figure. You must show all your work to receive full credit

Answer 1

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

$CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(11, 0) = (x_1, y_1)$

$D(6, -3) = (x_2, y_2)$

$CD = \sqrt{(6 - 11)^2 + (-3 - 0)^2}$

$CD = \sqrt{(-5)^2 + (-3)^2}$

$CD = \sqrt{25 + 9} = \sqrt{34}$

$CD = 5.8 units$ (nearest tenth)

DE = |6 - 4| = 2 units

$EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$E(4, -3) = (x_1, y_1)$

$F(0, -6) = (x_2, y_2)$

$EF = \sqrt{(0 - 4)^2 + (-6 -(-3))^2}$

$EF = \sqrt{(-4)^2 + (-3)^2}$

$EF = \sqrt{16 + 9} = \sqrt{25}$

$EF = 5 units$

$FA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$F(0, -6) = (x_1, y_1)$

$A(5, -8) = (x_2, y_2)$

$FA = \sqrt{(5 - 0)^2 + (-8 -(-6))^2}$

$FA = \sqrt{(5)^2 + (-2)^2}$

$FA = \sqrt{25 + 4} = \sqrt{29}$

$FA = 5.4 units$ (nearest tenth)

Perimeter = 6 + 8 + 5.8 + 2 + 5 + 5.4

= 32.2 units