Is it possible to take a cross section of a tetrahedron and get an octagon? Why or why not?

A.) Yes, because an octagon has eight sides, which is twice the number of faces on a tetrahedron.

B.) Yes, because a tetrahedron is symmetric about its center.

C.) No, because the only cross section that can result from a tetrahedron is a triangle.

D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

Answer: D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

Question

Mathematics

Lawrence Martinez

6 September, 09:46

Is it possible to take a cross section of a tetrahedron and get an octagon? Why or why not?

A.) Yes, because an octagon has eight sides, which is twice the number of faces on a tetrahedron.

B.) Yes, because a tetrahedron is symmetric about its center.

C.) No, because the only cross section that can result from a tetrahedron is a triangle.

D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

Answer: D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

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Answers (1)

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Julia Thornton · Answer 1

Answer: The correct answer is Choice D.

A tetrahedron is another name for a triangular prism. When you look at a tetrahedron it only has 4 different sides. If you take a cross section, the largest number of sides that you could have would be 4. There is no way to get an 8 sided octagon.