Problem #1929
1929.

A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?
This problem is copyrighted by the American Mathematics Competitions.

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Instructions for entering answers:
 Reduce fractions to
lowest terms and enter in the form 7/9.
 Numbers involving pi should be written as 7pi or 7pi/3
as appropriate.
 Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
 Exponents should be entered in the form 10^10.
 If the problem is multiple choice, enter the appropriate
(capital) letter.
 Enter points with parentheses, like so: (4,5)
 Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
NOT 0+2i).
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