SOLUTION: Find the surface area of a tetrahedran when the slant height is 10 in?

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Question 1001137: Find the surface area of a tetrahedran when the slant height is 10 in?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the surface area of a highlight%28tetrahedron%29 when the slant height is 10 in?
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Probably,  you mean a regular tetrahedron which has all edges congruent?
(Otherwise the question has no a unique answer . . . ).

Why do not formulate it directly,  clearly and explicitly?  Why I should do it instead of you?

Such a tetrahedron has four faces,  and each of them is a regular triangle with the altitude of  10 in.
Hence,  the base of each such a triangle is of  %282%2A10%29%2Fsqrt%283%29 in.  (It is the length of the edge of the regular tetrahedron).

Then the area of a single triangle  (of a single face)  is  1%2F2.20%2Fsqrt%283%29.10 = 100%2Fsqrt%283%29  square inches.

Hence,  the surface are of the tetrahedron is  %284%2A100%29%2Fsqrt%283%29 = 400%2Fsqrt%283%29  in%5E2.