Area of a Parallelogram
In this activity you are going to explore the area of a parallelogram, and how we can work out the area of any parallelogram.
The red point changes the height of the parallelogram. The orange point changes the base length of the parallelogram. The green point changes the slope of the sides of the parallelogram. The blue point "squeezes" the parallelogram. The area of the parallelogram is given.
The red point changes the height of the parallelogram. The orange point changes the base length of the parallelogram. The green point changes the slope of the sides of the parallelogram. The blue point "squeezes" the parallelogram. The area of the parallelogram is given.
1) If you were to move the green point one square to the right, what would the area of the new parallelogram be?
Now move the green point to check your prediction. Were you correct?
What does this tell us about parallelograms with the same height and base length?
Now move the green point to check your prediction. Were you correct?
What does this tell us about parallelograms with the same height and base length?
2) What will happen to the area of the parallelogram if you increase the base length by moving the orange point?
Move the orange point to check your prediction. Were you correct?
How is the base length of a parallelogram related to the area?
Move the orange point to check your prediction. Were you correct?
How is the base length of a parallelogram related to the area?
3) How will changing the height by moving the red point affect the area of the parallelogram?
Move the red point to check your prediction. Were you correct?
How does the height of a parallelogram affect the area?
Move the red point to check your prediction. Were you correct?
How does the height of a parallelogram affect the area?
4) How will moving the blue point affect the area of the parallelogram?
Move the blue point to check your prediction. Were you correct?
Move the blue point to check your prediction. Were you correct?
Using all the information you have worked out, come up with a formula (in words or algebra) to calculate the area of any parallelogram.
Ideas for Teachers
This activity is designed for students to use themselves to explore the area of parallelograms. Getting them to investigate in the order above should slowly get them to see the links. It would make a good homework, for them to describe the process and thoughts they had in finding the formula.
You could also use this in front of a class, by asking them what they think will happen to the area before you move various points, then show them what happens. See if some of your students can spot which distances have an effect on the area.
By setting the shape as a rectangle before you start, you can then show how a parallelogram is just a skewed rectangle.
An extension: can you make a rhombus?
This activity is designed for students to use themselves to explore the area of parallelograms. Getting them to investigate in the order above should slowly get them to see the links. It would make a good homework, for them to describe the process and thoughts they had in finding the formula.
You could also use this in front of a class, by asking them what they think will happen to the area before you move various points, then show them what happens. See if some of your students can spot which distances have an effect on the area.
By setting the shape as a rectangle before you start, you can then show how a parallelogram is just a skewed rectangle.
An extension: can you make a rhombus?
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