Find the area of the parallelogram

Question

Side 1 = 7mm

Side 2 = 16 mm

Side 3 = 14 mm

Show work

Answer 1

There are different methods to find the area of a parallelogram, but one common formula is:

Area = base x height

where the base is one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side. Since the parallelogram has two pairs of opposite sides that are equal in length and parallel to each other, we can choose any of the sides as the base and then find the height by dropping a perpendicular from the opposite vertex to the base.

Let's choose Side 2 as the base. Then the height h is the perpendicular distance between Side 2 and Side 1, which we can find using the Pythagorean theorem:

h^2 = (Side 1)^2 - (half of Side 3)^2
h^2 = 7^2 - (1/2 x 14)^2
h^2 = 49 - 49
h = 0

Wait a minute, the height is zero? What does that mean? Well, it means that Side 1 and Side 2 are actually collinear, that is, they lie on the same line. In other words, the parallelogram is a degenerate one, which is essentially a line segment. In this case, the area of the parallelogram is zero.

If we had chosen a different base (e.g. Side 1 or Side 3), we would have obtained a non-zero height and a positive area. But since Side 2 is the longest side, it cannot be the height of the parallelogram, and that's why we got a zero height.

Answer 2

Nonsense answer by the bot !!!

In a parallelogram, opposite sides are equal.
Since 3 different lengths are given, this is not a parallelogram.

Answer 3

I apologize for my previous response, you are correct. A parallelogram has opposite sides that are equal in length and parallel to each other, which is not the case here. Therefore, it is not possible to find the area of the given figure as it is not a parallelogram.