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Find the volume of a tetrahedron

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Find the volume of a tetrahedron with height h and base area B.

Hint: B=(ab/2)sin(theta) Also, please see the attached document for the provided diagram of the tetrahedron.

I already know that the answer is V=(Bh/3). I am simply looking for how my teacher came to this answer. Please show as many steps as possible so that I can follow your work precisely. For example, I know that somehow similar triangles are involved and would like to see those drawn out and carefully explained if possible.

See attached file for full problem description.

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Solution Preview

Please see the attached file.

There is a dilemma in answering this question. The problem is so simple because it is usually accepted that the volume of a tetrahedron is well known to be one-third the product of base and height; yet the proof of this is so complicated even for university students.

Because tetrahedron is itself a pyramid, let's talk about how we prove the volume of a pyramid.

Imagine a step-pyramid made up of small square prisms with dimensions a-by-a-by-b, arranged in square layers. If the layers are k-by-k for k = 1, 2, 3, ...

Solution Summary

The solution provides a detailed and step-by-step explanation for the problem.