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

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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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