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Problem 321: (2015 AMC 12b, 16)
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? $\textbf{(A)}\; 18 \qquad$ $\textbf{(B)}\; 162 \qquad$ $\textbf{(C)}\; 36\sqrt{21} \qquad$ $\textbf{(D)}\; 18\sqrt{138} \qquad$ $\textbf{(E)}\; 54\sqrt{21}$
Solution
Exercise 321: Solution
A regular hexagon with sides of length $4$ has an isosceles triangle attached to each side. Each of these triangles has two sides of length $5$. The isosceles triangles are folded up to make a pyramid with the hexagon as its base. What is the volume of the pyramid?
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