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Turkish NMO First Round - 1999 P-17 (Geometry)

Source:

July 3, 2012
geometry3D geometrypyramidrectangle

Problem Statement

In a regular pyramid with top point T T and equilateral base ABC ABC, let P P, Q Q, R R, S S be the midpoints of [AB] \left[AB\right], [BC] \left[BC\right], [CT] \left[CT\right] and [TA] \left[TA\right], respectively. If \left|AB\right| \equal{} 6 and the altitude of pyramid is equal to 215 2\sqrt {15}, then area of PQRS PQRS will be
<spanclass=′latex−bold′>(A)</span> 415<spanclass=′latex−bold′>(B)</span> 82<spanclass=′latex−bold′>(C)</span> 83<spanclass=′latex−bold′>(D)</span> 65<spanclass=′latex−bold′>(E)</span> 92<span class='latex-bold'>(A)</span>\ 4\sqrt {15} \qquad<span class='latex-bold'>(B)</span>\ 8\sqrt {2} \qquad<span class='latex-bold'>(C)</span>\ 8\sqrt {3} \qquad<span class='latex-bold'>(D)</span>\ 6\sqrt {5} \qquad<span class='latex-bold'>(E)</span>\ 9\sqrt {2}
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