30 square units.
The area of a parallelogram is
A= bh
where
A = area
b = base
h = height
Any side of a parallelogram can be used as the base. The height of a parallelogram is a perpendicular line from the base to the opposite side of the parallelogram. If needed, you can replace the opposite line segment with a line that overlays the line segment and continues to infinity in both directions.
Given the 4 points, the line segments (4,1) to (10,1) and (8,-4) to (2,-4) are the most interesting. Both of those lines have a slope of 0, which makes finding the distance between those two lines trivial. The height is simply the difference in their y-coordinate values. So
h = 1 - (-4) = 1 + 4 = 5
And the length of the base is the difference between their x-coordinates. (You can use either line for the base). So
b = 10 - 4 = 6
So the area is
A = bh
A = 6 * 5
A = 30
