Question 1001137
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Find the surface area of a {{{highlight(tetrahedron)}}} 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  {{{(2*10)/sqrt(3)}}} in.  (It is the length of the edge of the regular tetrahedron). 


Then the area of a single triangle  (of a single face)  is  {{{1/2}}}.{{{20/sqrt(3)}}}.{{{10}}} = {{{100/sqrt(3)}}}  square inches. 


Hence,  the surface are of the tetrahedron is  {{{(4*100)/sqrt(3)}}} = {{{400/sqrt(3)}}}  {{{in^2}}}.