ACT Math : How to find the diagonal of a tetrahedron

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #74 : Solid Geometry

Calculate the diagonal of a regular tetrahedron (all of the faces are equilateral triangles) with side length .

Possible Answers:

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  where s is the side length, so we can put  into this formula:

which gives us the correct answer.

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