Answer:
The area is equal to [tex]8\ units^{2}[/tex]
Step-by-step explanation:
we have
A(0, 0), B(2, -2), C(0, -4), D(-2, -2)
Plot the figure
The figure is a square (remember that a regular polygon has equal sides and equal internal angles)
see the attached figure
The area of the square is
[tex]A=AB^{2}[/tex]
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}[/tex]
[tex]AB=\sqrt{(-2)^{2}+(2)^{2}}[/tex]
[tex]AB=\sqrt{8}[/tex]
[tex]AB=2\sqrt{2}\ units[/tex]
Find the area of the square
[tex]A=(2\sqrt{2})^{2}[/tex]
[tex]A=8\ units^{2}[/tex]
