Answer:
Area: 30
Step-by-step explanation:
The area of a rectangle is given by the product between length (L) and width (W) of the rectangle:
[tex]A=L\cdot W[/tex]
Here we have to find the length and the width of the rectangle.
We know the 4 vertices of the rectangle:
A (1,2)
B (5,0)
C (2,-6)
D (-2,-4)
The length can be calculated as the distance between two consecutive points of the rectangle. Choosing A and B, we find:
[tex]L=|AB|=\sqrt{(5-1)^2+(0-2)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16+4}=4.47[/tex]
While the width can be calculating as the distance between the following pair of consecutive points, therefore the distance between B and C:
[tex]W=|BC|=\sqrt{(2-5)^2+(-6-0)^2}=\sqrt{3^2+(-6)^2}=\sqrt{9+36}=6.71[/tex]
And therefore, the area of hte rectangle is:
[tex]A=L\cdot W=(4.47)(6.71)=30[/tex]
