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24 votes
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How to justify formula for area of triangle (or parallelogram)

Remember that this is an explanation, not a proof. You don't need to define precisely how to construct the encompassing rectangle. Just demonstrate drawing an encompassing rectangle and have the 8-...
Justin Skycak's user avatar
14 votes

How to justify formula for area of triangle (or parallelogram)

As requested, a version without the encompassing rectangle. (Or at least one that has less algebra.) The initial triangle with base $b$ and height $h$: Double it, to get a parallelogram with twice ...
Adam's user avatar
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14 votes

How to justify formula for area of triangle (or parallelogram)

If you do want to deal with a triangle whose known base has an obtuse angle at one end (so that the height is not located between the endpoints of this base), you can use subtraction. I want the area ...
Sue VanHattum's user avatar
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11 votes

How to justify formula for area of triangle (or parallelogram)

An alternative explanation, one formula to rule them all, so to speak: There is a single formula that comprises the areas of a rectangle, parallelogram, trapezoid and triangle: $\qquad$The area equals ...
user1815's user avatar
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5 votes

How to justify formula for area of triangle (or parallelogram)

I do recommend going through the rectangles and parallelograms, but I just want to note that your intuition about starting with a right triangle and moving the top around is Cavalieri's principle and ...
Tommi's user avatar
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4 votes

Can we define length and perpendicularity not via an inner product?

Given this is an ED forum and you claimed (in comment replies) that you felt it was better at math ed, than at math non-ed, I'm replying to the EDUCATIONAL ASPECTS of your proposal (where I am better ...
guest troll's user avatar
2 votes

Can we define length and perpendicularity not via an inner product?

Here is an alternative way to model Euclidean geometry without appealing to Pythagorean theorem in any form or disguise. Start with a normed vector space $V$ and postulate that for every vector $u$ ...
tekhnus's user avatar
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