How to find the diagonal of a tetrahedron - ACT Math
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Question
Calculate the diagonal of a regular tetrahedron (all of the faces are equilateral triangles) with side length 
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Calculate the diagonal of a regular tetrahedron (all of the faces are equilateral triangles) with side length
Answer
The diagonal of a shape is simply the length from a vertex to the center of the face or vertex opposite to it. With a regular tetrahedron, we have a face opposite to the vertex, and this basically amounts to calculating the height of our shape.
We know that the height of a tetrahedron is 
where s is the side length, so we can put 
into this formula:
which gives us the correct answer.
The diagonal of a shape is simply the length from a vertex to the center of the face or vertex opposite to it. With a regular tetrahedron, we have a face opposite to the vertex, and this basically amounts to calculating the height of our shape.
We know that the height of a tetrahedron is
which gives us the correct answer.
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