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?

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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Comments

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

X X - 2 years, 8 months ago

Ok, thanks

Zoe Codrington - 2 years, 8 months ago

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

Zoe Codrington - 2 years, 7 months ago

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

Krishna Karthik - 2 years, 7 months ago

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

Krishna Karthik - 2 years, 7 months ago

I know this is messy, but please?

Zoe Codrington - 2 years, 8 months ago

X X - 2 years, 8 months ago

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 - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$