Answer:
C. 12.48 units
Step-by-step explanation:
Perimeter of the trapezoid = DE + EF + FG + GD
DE = |-2 - 1| = 3 units
FG = |-3 - 2| = 5 units
Find EF and GD using distance formula
✔️Distance between E(1, 3) and F(2, 1):
[tex] EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
(x1, y1) = (1, 3)
(x2, y2) = (2, 1)
Substitute
[tex] EF = \sqrt{(2 - 1)^2 + (1 - 3)^2} [/tex]
[tex] EF = \sqrt{(1)^2 + (-2)^2} [/tex]
[tex] EF = \sqrt{1 + 4} [/tex]
[tex] EF = \sqrt{5} [/tex]
[tex] EF = 2.24 units [/tex]
✔️Distance between G(-3, 1) and D(-2, 3):
[tex] GD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
(x1, y1) = (-3, 1)
(x2, y2) = (-2, 3)
Substitute
[tex] GD = \sqrt{(-2 -(-3))^2 + (3 - 1)^2} [/tex]
[tex] GD = \sqrt{(-1)^2 + (2)^2} [/tex]
[tex] GD = \sqrt{1 + 4} [/tex]
[tex] GD = \sqrt{5} [/tex]
[tex] GD = 2.24 units [/tex]
✅Perimeter = 3 + 2.24 + 5 + 2.24 = 12.48 units
