Equilateral Triangles

I found that the area of an equilateral triangle is sqrt(3)xS^2/4 where S is the side length But if I put it in a square, shouldn't the area be s^2/2?

Note by Zoe Codrington
1 month, 1 week ago

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If you put it in a square, the top vertice won't touch the side of the square.

X X - 1 month, 1 week ago

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Ok, thanks

Zoe Codrington - 1 month ago

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Did anyone else get this as their childhood interpretation of the A=bh/2 proof with equalateral triangles? I did.

Zoe Codrington - 1 week, 6 days ago

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@Zoe Codrington It is impressive to do it with geometry; it requires a very visual brain.

Krishna Venkatraman - 1 week, 3 days ago

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@Zoe Codrington no, I better understood it with calculus. I am no geometer. I like to visualise it using functions and Cartesian graphs.

Krishna Venkatraman - 1 week, 3 days ago

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X X - 1 month, 1 week ago

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But is it possible to somehow prove without using Pythagoras Theorem or common sense? Edit:I just worked out the proof, but if you have ways to prove it other than the angles of an iscoceles triangle and possibly angles of an equaliteral triangle it would be interesting to hear.

Zoe Codrington - 1 month ago

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I know this is messy, but please?

Zoe Codrington - 1 month, 1 week ago

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