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We are tasked with finding the volume of a right tetrahedron with known dimensions. The dimensions provided in the image are:

- The edge between points \( x \) and \( y \) is 100 units,
- The edge between points \( y \) and \( z \) is 96 units,
- The height from \( z \) to the base is 28 units.

The general formula for the volume of a tetrahedron is:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

The base here is a right triangle with sides 100 (from \( x \) to \( y \)) and 96 (from \( y \) to \( z \)). We can calculate the area of this triangular base using the formula for the area of a triangle:

\[
\text{Area of base} = \frac{1}{2} \times \text{base} \times \text{height}
\]

The height of the tetrahedron is given as 28 units (from point \( z \) perpendicular to the base). Now, let's compute the volume step by step. I'll perform the calculations now.The volume of the given right tetrahedron is \( 44,800 \) cubic units.

Would you like further details on the steps, or do you have any other questions?

Here are 5 related questions to expand on this:

1. How does the formula for the volume of a tetrahedron change for irregular tetrahedrons?
2. What are the other methods to calculate the volume of polyhedra?
3. How would the volume change if the dimensions were scaled by a factor of 2?
4. Can you derive the formula for the volume of any tetrahedron from vector operations?
5. How can you apply integral calculus to calculate the volume of more complex 3D shapes?

**Tip:** Understanding the geometric properties of basic shapes like tetrahedrons can help in visualizing and solving more complex 3D problems.

Find the volume of the given right tetrahedron. The dimensions are: the edge between points x and y is 100 units, the edge between points y and z is 96 units, and the height from z to the base is 28 units.

This problem explains how to find the volume of a right tetrahedron with base dimensions of 100 and 96 units, and a height of 28 units. Follow the steps to calculate the area of the triangular base and use the volume formula for the tetrahedron. Suitable for students in Grades 10-12.

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