In this lesson, students recall the defining attributes of parallelograms and other properties that follow from that definition. Students then use reasoning strategies from earlier work to find areas of parallelograms.

One approach for finding the area of a parallelogram is to decompose the parallelogram and rearrange the pieces into a rectangle. Another is to enclose the parallelogram in a rectangle of the same height and then subtract the area of the extra regions—two right triangles that can be rearranged into a rectangle.

By working with various parallelograms, students begin to see that the shape of certain parallelograms may encourage the use of certain strategies. For instance, a parallelogram that is narrow and stretched out may be cumbersome to decompose and rearrange. Enclosing it in a rectangle and subtracting the areas of the two extra pieces might be preferable.

Through repeated reasoning, students begin to see regularity (MP8): parallelograms have related rectangles that can be used to find their area. Students also describe the process of finding the area of a parallelogram more generally, which prepares them to express that process as a formula.

A note about notation:

When recording students’ solutions and reasoning in this lesson, consider using the “dot” notation instead of the “cross” notation to indicate multiplication. Explain that the  symbol and the symbol both represent multiplication. Doing so familiarizes students with the use of the notation before they see it in student-facing materials.