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## cutidede 2 years ago why is the area of a rectangle base x height? Why is a non-rectangular parallelogram base x height and is this true?

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1. richyw

yes this is true. You can show it many ways. But basically if you consider the parallelogram made up of two vectors in a plane. The area is the cross product of these vectors. If you put b so that it is in the direction of one of the axis you have h as the component of the second vector in the opposite plane. So the cross product would give you base*height.

2. AccessDenied

Area is measured in a fancy derived unit: "squared (unit)". I think it would be easiest to show if you split the rectangle into "unit squares;" i.e., they are squares of a side length of one unit. |dw:1352689557487:dw| A fast way to count the number of squares here inside the rectangle is simply multiplying your number of columns by your number of rows. Thus, base times the height. A parallelogram is quite interesting as well. If we have a parallelogram here, consider rearranging things. |dw:1352689759240:dw| We only move pieces around, so the area has not changed. However, we effectively can fill the gap on one side of the parallelogram with the other side! Thus, it makes a rectangle. We already know the routine from there: base x height. :)

3. cutidede

okay thanks. i understand it better now.

4. AccessDenied

You're welcome! :)

5. cutidede

could u help me with my other math problem about tennis balls

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