Answer:
Area of this parallelogram: 35.
Explanation:
What's the equation for the area A of a parallelogram?
A = b · h,
where
- b is the length of the base, and
- h is the length of the height on that base.
Plot the four vertices on a cartesian plane. Two opposite sides of this parallelogram are parallel to the x-axis. As a result, the length of the base is the same as the difference in x-coordinates between two vertices on that side. As seen on the diagram, the length of this base is b = 2 - (-5) = 7.
The height on either of those two sides will be normal to the x-axis and parallel to the y-axis. The length of those heights will be the same as the difference in y-coordinates between two vertices, one on each line. As seen on the diagram, the length of the height on base b is h = 4 - (-1) = 5.
Area of this parallelogram:
A = b · h = 5 × 7 = 35.