Area of Parallelograms

Warmup

Activity #1

Find the Area of a Parallelogram.

Although it is impossible to fit a whole number of unit squares into a rectangle that is 5 3/4 units long and √7 units wide, for example, we declare, nonetheless, that the area of such a rectangle is the product of these two numbers.

•  Move the slider below the parallelogram back and forth to change the value of the base.
• Leave the slider at the right end.
•  Move the vertical slider up and down the scale to change the value of the height.
• Leave the slider at the top.
• Move the Hint slider back and forth to toggle between a parallelogram and a square.

• Answer the questions below.

Activity #2

Explore the Maximum Area of a Rectangle Given a Perimeter.

In the following activity, we are going to be working with different dimensions of a rectangle with a fixed perimeter. Our goal is to find out which dimension will give us the greatest area. This is an important application to land developers. Follow the instructions below.

• Move the slider to adjust the rectangles width. ​
• Record the widths & areas for w = 15, 30, 45, 60, 75, 90, 105, 120, 135. ​
• Observe when the areas are the same. ​
• Observe the maximum area.

• Answer the questions below.

(1.) How is the length being determined?

(2.) Describe the rectangle that has the maximum area.

Tyler was trying to find the area of the parallelogram below.

• Move the slider to see how he did it.​

Elena was also trying to find the area of a parallelogram.

• Move the slider to see how she did it.

• Answer the questions below.

(1.) How are the two strategies for finding the area of a parallelogram the same?

(2.) How they are different?

Challenge #1

Here are the areas of three parallelograms. Use them to find the missing length (labeled with a “?”) on each parallelogram. A: 10 square units, B: 21 square units, C: 25 square units.

Challenge #2

Challenge #3