Answer:
125.5 units
Step-by-step explanation:
The vertices of the composite figure has been named A to F.
*See attachment below.
Thus, Perimeter of ABCDEF = [tex] \overline{AB} + \overline{BC} + \overline{CD} + \overline{DE} + \overline{EF} + \overline{FA} [/tex]
[tex] \overline{AB} [/tex] = |-12 - 6| = 18 units
[tex] \overline{BC} [/tex] = |-12 - 3| = 15 units
[tex] \overline{CD} [/tex] = |6 - 15| = 9 units
[tex] \overline{DE} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(24 - 15)^2 + (18 - 3)^2} = \sqrt{9^2 + 15^2} = \sqrt{81 + 225} = \sqrt{306} = 17.5 units [/tex]
[tex] \overline{EF} [/tex] = |-12 - 24| = 36 units
[tex] \overline{FA} [/tex] = |-12 - 18| = 30 units
Thus, Perimeter of ABCDEF = 18 + 15 + 9 + 17.5 + 36 + 30 = 125.5 units
