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Q&A #19360 |
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Hi, Meridith -- Thanks for writing to T2T. You could have students experiment with four straws threaded together, so they can be shaped into a parallelogram. Use two pairs of equal lengths, maybe two 5" and two 3". If they shape them into a rectangle first on a sheet of 1/2" graph paper, they will be able to see where the area of a rectangle (a special type of parallelogram) comes from, which is equivalent to that of the parallelogram in this case, since the vertical and "slanted" lengths are identical. Then squash the shape into a parallelogram with a vertical height of 2.5" and verify the area equation result with the observable area on the graph paper. The vertical height decreases while the base and slanted lengths stay constant. Continue squashing and measuring. Imagine slicing off the right triangle created on one end by dropping the height from a vertex at the top to the base. Slide it to the opposite end of the parallelogram, and you will create a rectangle with area base * height. Squashing the parallelogram until the height is nearly zero shows that the area shrinks as the the height decreases, while the side lengths have remained constant. This could also be done by drawing parallelograms on graph paper, keeping the base constant and changing the vertical height gradually, and measuring area. Using our Math Tools service, http://mathforum.org/mathtools/, I found an applet that demonstrates this concept very well. You can drag the vertices and see the relationships among the dimensions and area as you change different aspects. http://www.mathopenref.com/parallelogramarea.html This one is simpler, but not as flexible: http://illuminations.nctm.org/ActivityDetail.aspx?ID=108 I hope this makes sense. Good luck. Please write again if you have more questions. I'd love to hear about your experience if you decide to try any of this. -Claire, for the T2T service
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