• We can choose any side of a parallelogram as the base. Both the side selected (the segment) and its length (the measurement) are called the base.

• If we draw any perpendicular segment from a point on the base to the opposite side of the parallelogram, that segment will always have the same length. We call that value the height. There are infinitely many segments that can represent the height!

Here are two copies of the same parallelogram.

2 copies of the same parallelogram. On the left, base = 6 units. Corresponding height = 4 units. On the right, base = 5 units. Corresponding height = 4.8 units. For both, 3 different segments are shown to represent the height.

For both, three different segments are shown to represent the height. We could draw in many more!

No matter which side is chosen as the base, the area of the parallelogram is the product of that base and its corresponding height. We can check this:

We can see why this is true by decomposing and rearranging the parallelograms into rectangles.

Notice that the side lengths of each rectangle are the base and height of the parallelogram. Even though the two rectangles have different side lengths, the products of the side lengths are equal, so they have the same area! And both rectangles have the same area as does the parallelogram.

We often use letters to stand for numbers. If is a base of a parallelogram (in units), and is the corresponding height (in units), then the area of the parallelogram (in square units) is the product of these two numbers:

Notice that we write the multiplication symbol with a small dot instead of a symbol. This is so that we don’t get confused about whether means multiply, or whether the letter is standing in for a number.