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2016 AIME I Problems/Problem 4

Revision as of 17:04, 4 March 2016 by Ohmcfifth (talk | contribs) (Created page with "==Problem== A right prism with height <math>h</math> has bases that are regular hexagons with sides of length 12. A vertex <math>A</math> of the prism and its three adjacent v...")
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Problem

A right prism with height $h$ has bases that are regular hexagons with sides of length 12. A vertex $A$ of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain $A$ measures $60$ degrees. Find $h^2$.

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