Question

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

Answer 1

32.2 units

Explanation:

The perimeter of the figure = AB + BC + CD + DE + EF + FA

AB = |5 - 11| = 6 units

BC = |-8 - 0| = 8 units

`CD = √((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 = √((6 - 11)^2 + (-3 - 0)^2)`

`CD = √((-5)^2 + (-3)^2)`

`CD = √(25 + 9) = √(34)`

`CD = 5.8 units` (nearest tenth)

DE = |6 - 4| = 2 units

`EF = √((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 = √((0 - 4)^2 + (-6 -(-3))^2)`

`EF = √((-4)^2 + (-3)^2)`

`EF = √(16 + 9) = √(25)`

`EF = 5 units`

`FA = √((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 = √((5 - 0)^2 + (-8 -(-6))^2)`

`FA = √((5)^2 + (-2)^2)`

`FA = √(25 + 4) = √(29)`

`FA = 5.4 units` (nearest tenth)

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

= 32.2 units