MathDB
Hexagonal Pyramid

Source: 2015 AMC 12B #16

February 26, 2015
geometry3D geometrypyramidsymmetryPythagorean TheoremAMC

Problem Statement

A regular hexagon with sides of length 66 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 88. 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?
<spanclass=latexbold>(A)</span>18<spanclass=latexbold>(B)</span>162<spanclass=latexbold>(C)</span>3621<spanclass=latexbold>(D)</span>18138<spanclass=latexbold>(E)</span>5421<span class='latex-bold'>(A) </span>18\qquad<span class='latex-bold'>(B) </span>162\qquad<span class='latex-bold'>(C) </span>36\sqrt{21}\qquad<span class='latex-bold'>(D) </span>18\sqrt{138}\qquad<span class='latex-bold'>(E) </span>54\sqrt{21}