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Math Help - Regular pyramid

  1. #1
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    Regular pyramid

    Hi!
    Yesterday we had a exercise in geometry, it was said:
    A regular triangle pyramid with all of its edges 5cm long. There is a smaller triangle that is cutting the edge in half. Need to calculate volume and full surface area.
    Here is a small picture of the figure -


    As far as I could figure out this one, the bigger triangle is 2 times bigger then the smaller one, area is 2^2 times bigger.
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  2. #2
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    Quote Originally Posted by regdude View Post
    Hi!
    Yesterday we had a exercise in geometry, it was said:
    A regular triangle pyramid with all of its edges 5cm long. There is a smaller triangle that is cutting the edge in half. Need to calculate volume and full surface area.
    Here is a small picture of the figure -


    As far as I could figure out this one, the bigger triangle is 2 times bigger then the smaller one, area is 2^2 times bigger.
    correct, and the volume of the larger would be 2^3 times as large.

    here is a link to all kinds of good info re: tetrahedrons ...

    Tetrahedron -- from Wolfram MathWorld
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  3. #3
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    The weirdest thing about this exercise is one of its answer - 21.875*sqrt(3) (I think, but something like that).
    Tried to mark one of the triangles edge as "x" to see if somewhere I can get an equation that would cancel out those "x".
    Only equation that I saw to have division was this:
    H1^2 / H2^2 = S1 / S2
    height squares are proportional to triangle areas.
    Another way to get rid of "x" is to have right triangles and use this simple equation: b^2 = a^2 - c^2
    But couldn't find any right triangle that would give me a^2 on both sides.
    Last edited by regdude; November 27th 2010 at 07:03 AM.
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