Answer:
18 square units.
Step-by-step explanation:
Area of the triangle = ½*AB*CD
First of all, find the length of AB and CD using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
A(-6, 2) => (x1, y1)
B(3, 2) => (x2, y2)
[tex] AB = \sqrt{(3 -(-6))^2 + (2 - 2)^2} [/tex]
[tex] AB = \sqrt{(9)^2 + (0)^2} = \sqrt{81} = 9 [/tex]
[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
C(-2, 6) => (x1, y1)
D(-2, 2) => (x2, y2)
[tex] CD = \sqrt{(-2 -(-2))^2 + (2 - 6)^2} [/tex]
[tex] CD = \sqrt{(0)^2 + (-4)^2} = \sqrt{16} = 4 [/tex]
AB = 9
CD = 4
Area of rectangle = ½*AB*CD = ½*9*4 = 9*2 = 18 square units.
