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April 19, 2015

April 19, 2015

Posted by **Lucas** on Tuesday, May 15, 2012 at 1:42am.

- geometry -
**Reiny**, Tuesday, May 15, 2012 at 8:43amthe 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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