Results 1 to 8 of 8

Math Help - Pyramid height problem

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    United States
    Posts
    14

    Pyramid height problem

    A pyramid has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e, If e = m, what is the value of h in terms of m?

    The answer I got was (m*sqrt(6))/3, but that's wrong
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Pyramid height problem

    Consider a right triangle whose horizontal leg runs from one of the vertices of the square base to the center of the base (it's length is half the diagonal of the square base), the vertical leg runs from the center of the base to the vertex of the pyramid (the altitude of the pyramid) and the hypotenuse is the edge of length e.

    So, you know the horizontal leg and the hypotenuse in terms of m, you may find the altitude using the Pythagorean theorem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,685
    Thanks
    446

    Re: Pyramid height problem

    ...
    Attached Thumbnails Attached Thumbnails Pyramid height problem-volume-surface-area-square-based-pyramid-equal-edges.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2012
    From
    United States
    Posts
    14

    Re: Pyramid height problem

    Thank you, but do you need the slant height? Also how did you get the slant height?
    i got up to the [m*sqrt(2)]/2 for the base diagonal, but could you explain how you got the same for the height?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Pyramid height problem

    You don't need the slant height, that was thrown in for good measure I am assuming.

    To find h, use the Pythagorean theorem:

    \left(\frac{m}{\sqrt{2}} \right)^2+h^2=m^2

    Now, solve for h.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2012
    From
    United States
    Posts
    14

    Re: Pyramid height problem

    OOOOH thank you! I didn't even realize
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    10
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Nov 2012
    From
    United States
    Posts
    14

    Re: Pyramid height problem

    [ root(2)*s ]/2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The height of a pyramid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 24th 2011, 01:52 PM
  2. Pyramid's height
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 3rd 2010, 10:49 AM
  3. Slant height of a pyramid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 11th 2010, 10:50 AM
  4. Replies: 1
    Last Post: March 31st 2010, 02:29 AM
  5. Height of Pyramid
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 21st 2008, 06:41 PM

Search Tags


/mathhelpforum @mathhelpforum