Answer:
Area: 30
Step-by-step explanation:
The area of a rectangle is given by
[tex]A=L\cdot H[/tex]
where
L is the length
H is the height
For the rectangle in this problem, we know the location of the 4 vertices:
A (1,2)
B (5,0)
C (2,-6)
D (-2,-4)
In order to find the length and the height of the rectangle, we have to find the distance between two consecutive pairs of points.
For instance, the length is the distance between A and B:
[tex]L=|AB|=\sqrt{(5-1)^2+(0-2)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}=4.47[/tex]
While the height is the distance between B and C:
[tex]H=|BC|=\sqrt{(2-5)^2+(-6-0)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9+36}=\sqrt{45}=6.71[/tex]
Therefore, the area of the rectangle is:
[tex]A=L\cdot H = (4.47)(6.71)=30[/tex]
