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March 27, 2017

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A tetrahedron is a triangular pyramid in which each face is an equilateral triangle. Calculate the volume of a tetrahedron that has all its edges 6 cm in length. Hint: You will need to know some geometry and trigonometry.

  • geometry - ,

    the height of the tetrahedron will hit the centroid of the base.
    and will be 2/3 of the way from the vertex.
    Length of median of base:
    m^2 + 3^2 = 6^2
    m= √27 =3√3
    so distance from vertex to centroid = (2/3)(3√3) = 2√3
    let the height of the pyramid be h
    h^2 + (2√3)^2 = 6^2
    h = √24 = 2√6

    area of base = (1/2)(6)(6)sin60°
    = 18√3/2 = 9√3

    volume of tetrahedron
    = (1/3) base x height
    = (1/3)(9√3)(2√6) = 18√2

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