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Question
Submitted by foobal on Wed, 2012-04-25 14:55
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Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.

Answer
Submitted by zext on Thu, 2012-04-26 01:44
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correct answer

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6-inch apothem, xxxxxxx x x x
an xxxxxxxxxxx triangle has 6 (30-60-90) triangles each with the xxxxxxxx side xxxxx xxx apothem xx length x x inch
xxxxxxxxx xxxxxxxx xx a is xx xxxxxxxx
sin xx = xxxxxxxxxxxxxxxxxxx x a/hyp = 6/hyp
0.5 = 6/hyp
xxxxxx = x
hyp x 12 xxxxxx
xxxx we need xxxxxx xx xxxx side ,
cos xx x base/hypotenuse = xxxxxxx
xxxxxxxxx x xxxxxxx
xxxxxxxxxxx x xxxx
xxxxxxxx = xxxx
Now, xxxx xx xxxxxx small xxxxxxxx is
xxxxxxxxxxxxxxxxxxxx = 18sqrt(3) sq in
xxxx xxxxxxxxxxx triangle has x such xxxxx xxxxxxxxxx
xxxxxx
area xx equilateral xxxxxxxx = 6*(18sqrt(3)) x xxxxxxxxxx xx in.
= xxxxx sq. xxx xxxxxxx xx xxxxxxx xxxxxx


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