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Why is the area of parallelogram not equal to the product of the distances between the two pairs of parallel sides? A parallelogram is just a rectangle that has a triangle cut off from one side and added to the other; so then why is the area not equal to the product of the distances between the two pairs of parallel sides?

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  • $\begingroup$ No on the first because yes on the second $\endgroup$ – Hagen von Eitzen Oct 17 '19 at 8:02
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As you suggested, let's take a rectangle and cut a triangle from one side and add it to the other. Imagine the resulting parallelogram has two horizontal sides, and that the other two sides are "non-vertical" (else we'd still have a rectangle.) The distance between the two "non-vertical" sides would be measured perpendicularly to those sides; however the distance needed for the area would have to be measured horizontally, because that would have been the distance between those two sides when the shape was still a rectangle.

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  • $\begingroup$ Makes sense. Thanks @A.J. $\endgroup$ – Shreyas Thakur Oct 18 '19 at 6:17

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