Question

Determine the area of the parallelogram with vertices (4, 6, 2), (4, 7, 2), (9, 7, 2), and (9, 8, 2). Use the square root symbol '√' where needed to give an exact value for your answer.

Answer 1

5 square units

Explanation:

The parallelogram lies entirely in the plane z=2, so we can treat this as a 2-dimensional problem.

In the order given, the vertices do not define a parallelogram. Two of the sides are parallel, but the other two sides cross each other, for a net area of zero.

If we swap the order of the last two vertices, we get a parallelogram that has a base of 1 unit and a height of 5 units. Its area is ...

A = bh = 1·5 = 5 . . . square units