Problem:
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?
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Solution:
The distance from a vertex of the hexagon to its center is 6 . The height of the pyramid can be calculated by the Pythagorean Theorem using the right triangle with other leg 6 and hypotenuse 8 ; it is . The volume is then
The problems on this page are the property of the MAA's American Mathematics Competitions