You should plot these. I won't but I can see it's a square. Each vertex differs from the previous one by two units in the x direction and two in the y. Each of the squared sides given by the Pythagorean Theorem is the area,
[tex]A = 2^2+(-2)^2=8[/tex]
Choice D, not approximate.
Let's check a different way. Given the 2D vertices of a polygon in order, the area is given by the Shoelace Formula. The area is half the absolute value of the sum of cross products. We write the points shifted on top of each other for easy in calculation
(0,0),(2,-2),(0,-4),(-2,-2)
(2,-2),(0,-4),(-2,-2),(0,0)
A = \frac 1 2 | 0(-2) - (0)(2) + 2(-4)- -2(0) + 0(-2)-(-4)(-2) + -2(0) + -2(0) | = \frac 1 2 |-16| = 8 \quad\checkmark[/tex]
