Area of Parallelograms

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Is the Area of a Parallelogram found the same way as the area of a Rectangle?

• Click the sides of the parallelogram and the rectangle to see their lengths.​
• Check the “Dissect Parallelogram” box to decompose the parallelogram.
• Drag the blue sider to the right to transfer the parts of the rectangle.
• Check the “Conclusion” box.
• Check the “Answer” box.

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More Investigation on Finding the Area of a Parallelogram.

•  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.

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Exploring the Maximum Area of a Rectangle given a Perimeter.

(A). Exploring the Maximum Area of a Rectangle given a Perimeter.

• 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.

How is the length being determined? Describe the rectangle that has the maximum area.

(B). Tyler was trying to find the area of the parallelogram below. Move the slider to see how he did it.​

(C). Elena was also trying to find the area of a parallelogram. Move the slider to see how she did it.

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

(2). How they are different?

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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.

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