In this lesson, students learn about bases and heights of a parallelogram and generalize the process for finding the area of a parallelogram.

Students begin by comparing two strategies for finding the area of a parallelogram. This comparison sets the stage for seeing a rectangle that is associated with a parallelogram and for understanding bases and heights. 

Then students identify both a base and its corresponding height for given parallelograms and find their areas. Through repeated reasoning, students notice regularity in the process of finding the area of a parallelogram and express it as a formula in terms of base and height (MP8).

Next, students practice using the formula for the area of parallelograms for parallelograms shown both on and off a grid. They see that parallelograms with the same base and the same height have the same area because the products of those two numbers are equal, even if the parallelograms look very different.

A note about terminology:

The terms “base” and “height” are potentially confusing because they are sometimes used to refer to particular line segments, and sometimes to the length of a line segment or the distance between parallel lines. Furthermore, there are always two base-height pairs for any parallelogram, so asking for the base and the height is not, technically, a well-posed question. Instead, asking for a base and its corresponding height is more appropriate. In these materials, the words “base” and “height” mean the numbers unless it is clear from the context that it means a segment and that there is no potential confusion.

A note about notation:

In this lesson, students see the “dot” notation for multiplication in their materials for the first time. If needed, reiterate that both the symbol and the symbol represent multiplication.