Unlocking the Area of Parallelograms: From Rectangles to Amazing Transformations!
Lesson Description
Video Resource
Area of parallelograms intuition | Algebra I | High School Math | Khan Academy
Khan Academy
Key Concepts
- Area of a rectangle (base x height)
- Area of a parallelogram (base x height)
- Geometric transformation (moving a triangle to form a rectangle)
- Height of a parallelogram (perpendicular distance between base and opposite side)
Learning Objectives
- Students will be able to explain why the area of a parallelogram is base times height.
- Students will be able to calculate the area of a parallelogram given its base and height.
Educator Instructions
- Introduction (5 mins)
Begin by reviewing the formula for the area of a rectangle (Area = base x height). Ask students to recall how they learned this formula and why it works. Show a rectangle on the board or screen. - Video Viewing (7 mins)
Play the Khan Academy video "Area of parallelograms intuition". Instruct students to pay close attention to how the parallelogram is transformed into a rectangle. - Guided Discussion (8 mins)
After the video, lead a discussion about the transformation shown. Ask students to explain in their own words how the triangle was moved and why this proves the area formula for a parallelogram. - Practice Problems (10 mins)
Present students with several parallelogram problems, asking them to calculate the area. Include examples with different orientations and units of measurement. Encourage students to draw the height if it is not already provided. - Wrap-up (5 mins)
Summarize the key takeaways of the lesson: the area formula for parallelograms, the relationship between parallelograms and rectangles, and the importance of identifying the base and height correctly.
Interactive Exercises
- Area Calculation Worksheet
A worksheet with various parallelograms, each with different base and height measurements. Students calculate the area of each parallelogram. Include some parallelograms where the side length is given but not the height to trick students. - GeoGebra Parallelogram Transformation
Use a GeoGebra applet to allow students to interactively transform a parallelogram into a rectangle. This will provide a hands-on experience reinforcing the video's demonstration.
Discussion Questions
- How is a parallelogram similar to a rectangle?
- Why is the height of a parallelogram measured perpendicularly to the base?
- Can you think of any real-world examples of parallelograms?
Skills Developed
- Visual reasoning
- Problem-solving
- Application of formulas
Multiple Choice Questions
Question 1:
The area of a rectangle is found by multiplying the _____ and the _____. What two words fill in the blanks?
Correct Answer: Base, Height
Question 2:
What is the formula for the area of a parallelogram?
Correct Answer: Area = base x height
Question 3:
Why is the height of a parallelogram measured at a 90-degree angle (perpendicular) to the base?
Correct Answer: To find the shortest distance between the base and the opposite side.
Question 4:
A parallelogram has a base of 8 cm and a height of 5 cm. What is its area?
Correct Answer: 40 cm²
Question 5:
Imagine cutting a triangle off one side of a parallelogram and moving it to the other side. What shape do you create?
Correct Answer: Rectangle
Question 6:
Which of these is NOT needed to find the area of a parallelogram?
Correct Answer: The length of the diagonal
Question 7:
A parallelogram has an area of 60 square inches and a base of 10 inches. What is the height?
Correct Answer: 6 inches
Question 8:
Which of the following statements is TRUE about the area of a parallelogram and a rectangle with the same base and height?
Correct Answer: They have the same area.
Question 9:
The height of a parallelogram is always measured:
Correct Answer: Perpendicular to the base
Question 10:
A parallelogram has a base of 12 m and a height of 6 m. What is the area?
Correct Answer: 72 m²
Fill in the Blank Questions
Question 1:
The area of a parallelogram is found by multiplying the ______ by the ______.
Correct Answer: base, height
Question 2:
The height of a parallelogram is the perpendicular distance between the base and its _______ side.
Correct Answer: opposite
Question 3:
If you cut a triangle from one side of a parallelogram and move it to the other, you form a ______.
Correct Answer: rectangle
Question 4:
A parallelogram with a base of 7 cm and a height of 4 cm has an area of ______ cm².
Correct Answer: 28
Question 5:
The formula for the area of a parallelogram is Area = b x ______, where b is the base.
Correct Answer: h
Question 6:
The height must create a ________ degree angle with the base.
Correct Answer: 90
Question 7:
If a parallelogram has an area of 48 square meters and a height of 8 meters, then the base is ________ meters.
Correct Answer: 6
Question 8:
Transforming a parallelogram into a rectangle demonstrates that they have the same ______.
Correct Answer: area
Question 9:
The area is always in ________ units, such as cm² or m².
Correct Answer: square
Question 10:
The area of a parallelogram is the amount of _______ inside the parallelogram.
Correct Answer: space
Educational Standards
Teaching Materials
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