This activity allows students to practice finding and reasoning about the area of various parallelograms—on and off a grid. Students make sense of the measurements and relationships in the given figures and identify an appropriate pair of base-height measurements to use (the length of a side and that of a segment that is perpendicular to that side). Students learn to recognize that two parallelograms with the same base-height measurements (or with different base-height measurements but the same product) have the same area.

As they work individually, notice how students determine base-height pairs to use. As they work in groups, listen to their discussions and identify those who can explain how they found the area of each of the parallelograms.

In the digital version of the activity, students use an applet to create two parallelograms with the same area.

Use whole-class discussion to highlight three important points:

• We need base and height information to calculate the area of a parallelogram, so we generally look for the length of one side and the length of a perpendicular segment that connects that side to the opposite side. Other measurements may not be as useful.
• A parallelogram has two pairs of base and corresponding height. Both pairs produce the same area, so the product of one pair of numbers should equal the product of the other pair.
• Two parallelograms with different pairs of base and corresponding height can have the same area, as long as their products are equal. A 3-by-6 rectangle and a parallelogram with a base of 1 and a height of 18 will have the same area because .

To highlight the first point, consider asking:

• “The parallelograms in the first question show multiple measurements. How did you know which ones would help you find the area?”
• “Which pieces of information in Parallelograms B and C were not needed? Why not?”

To highlight the second point, select 1 or 2 students to share how they found the missing height in the second question. Emphasize that the product of 815 and that of 10 and the unknown h must be equal because both give us the area of the same parallelogram.

To highlight the last point, invite a few students to share their pair of parallelograms and how they know that the areas are equal. If not made explicit in students' explanations, stress that the base-height pairs must have the same product. Consider displaying the applet for all to see and using it to facilitate this discussion.