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posted by  Urgent SOS on 7/28/2009 11:30:30 PM  |  status: Closed  |  Earned Karma: 227

solid geometry

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A right pyramid with a vertex T and rectangular base PQRS. Given RS=8cm and ST=13cm, the volume of the pyramid in is?
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posted by wchau on 7/29/2009 11:50:15 AM  |  status: Live
Clarification Details:
If rectangle is not a square, then you need to provide the length . Otherwise there are infinitely number of pyramids satisfying the given conditions.
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posted by lawrence_tutor on 7/29/2009 6:09:52 AM  |  status: Live
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posted by Urgent SOS on 7/29/2009 11:34:54 AM  |  status: Live
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Response Details:
Question mentioned about rectangular base, how can we assume it as square?
As a rectangular base, any way to proof that QR=6cm?
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posted by wchau on 7/29/2009 11:56:38 AM  |  status: Live
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Response Details:


Since and are, respectively, the diagonal and a side of the square base of the given right pyramid, so triangle is a triangle, so .



From the diagram above, and are the center of the base and the height of the right pyramid. Thus is a right triangle. Applying the Pythagorean theorem to triangle , and so . It follows that the volume of the given pyramid is .
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