Where Did the 4 in the 30-60-90 Triangle Calculation Come From?

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SUMMARY

The discussion centers on the derivation of the '4' in the area calculation of a 30-60-90 triangle using the Pythagorean theorem. The user references a Khan Academy video that explains how the formula for the area involves the expression A = h²(1 - 1/4). The '4' arises from the calculation of the base of the triangle, specifically when determining the length of the base as half of the hypotenuse. This leads to the conclusion that the area formula incorporates this factor to accurately represent the triangle's dimensions.

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HenryKhais
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Im watching one of khan's videos:
http://www.youtube.com/watch?v=Qwet4cIpnCM&feature=player_embedded#at=468

And he's using the pythagorean theorem to solve height of a 30-60-90 triangle.
Prior to everything, I think I have a good understanding on how it all works, however, I still don't feel like I understand it fully.

From what I understand, pythagorean theorem's formula is: base^(2) x height^(2) = hypotenuse^(2).

Now if you watch the video and skip to the 8:00 mark, everything seems to make sense to me except the part where he adds '4' as the denominator under h^(2), nor do I understand how he got 'A=h^(2)(1 - 1/4).
Where did the 4 come from?

Sorry if this is an obvious question, I am self teaching and really just want to learn and fully understand it.

Thanks =)
 
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From the video at the 8 min mark,

[1/2*h]^2 = [1/2]^2*[h]^2 = 1/4*h^2 = h^2/4

Does this help?
 

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