Answer:
A = 20
P = 6√10
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(-3, 0) , B(3, 2)
[tex]AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}[/tex]
A(-3, 0), D(-2, -3)
[tex]AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
AB = CD and AD = BC
The area of a rectangle:
[tex]A=(AB)(AD)[/tex]
Substitute:
[tex]A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20[/tex]
The perimeter of a rectangle:
[tex]P=2(AB+AD)[/tex]
Substitute:
[tex]P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}[/tex]
