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Math Help - Simple Q: Are the Sides of a pyramid always of equal length?

  1. #1
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    Question Simple Q: Are the Sides of a pyramid always of equal length?

    This is a simple question however I do not know the answer to it and it's curiosity that has me posting this.

    *Are the sides of any pyramid, meeting the apex, the same length?

    So that includes every pyramid out there. Now to save confusion:

    I am not asking if every pyramid has equal sides of length as the obvious answer is no.

    I am asking In one particular pyramid (which has a base of any shape) are it's sides (the one's meeting the apex) always going to be the same length?

    So for example the sides in a square pyramid meeting the apex are the same length. Would this also be the case for a rectangular pyramid?

    Thanks
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  2. #2
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    Quote Originally Posted by Astar View Post
    This is a simple question however I do not know the answer to it and it's curiosity that has me posting this.

    *Are the sides of any pyramid, meeting the apex, the same length?

    So that includes every pyramid out there. Now to save confusion:

    I am not asking if every pyramid has equal sides of length as the obvious answer is no.

    I am asking In one particular pyramid (which has a base of any shape) are it's sides (the one's meeting the apex) always going to be the same length?

    So for example the sides in a square pyramid meeting the apex are the same length. Would this also be the case for a rectangular pyramid?

    Thanks
    1. It depends how you define a pyramid: It is a solid with at least 4 apices, bounded by plane areas. The base area can be of any shape (even a star like area is possible) and the surface area is composed by triangles.

    2. I've sketched 3 pyramids with identical base areas where the apex is perpendicular
    - to one vertex of the base area
    - to the centroid of the base area
    - to the midpoint of one side of the base area.

    3. By simple trigonometry you'll see that the lengthes of the edges of the surface are not necessarily equal.
    Attached Thumbnails Attached Thumbnails Simple Q: Are the Sides of a pyramid always of equal length?-versch_pyramidtyp.png  
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