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To solve this problem, we need to find the volume of the given right tetrahedron. A tetrahedron is a three-dimensional figure with four triangular faces. The formula for the volume \( V \) of a tetrahedron with a right-angle vertex can be expressed as:

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

In the provided diagram, the tetrahedron has the right-angle vertex at point \( z \), with three labeled edges forming a right triangle. These labeled edges provide the base and height for our calculations.

The base triangle lies in the \( xy \)-plane, where:
- The edge along the \( x \)-axis is 100 units.
- The edge along the \( y \)-axis is 96 units.

These two edges form a right triangle, so the area of this triangular base is:

\[
\text{Base Area} = \frac{1}{2} \cdot 100 \cdot 96
\]

The height of the tetrahedron is along the \( z \)-axis, which is 128 units.

Now, we can calculate the volume:

\[
V = \frac{1}{3} \cdot \text{Base Area} \cdot \text{Height}
= \frac{1}{3} \cdot \frac{1}{2} \cdot 100 \cdot 96 \cdot 128
\]

Let's compute this.The volume of the given right tetrahedron is \( 204800 \) cubic units.

Would you like a detailed breakdown of the steps, or do you have any further questions?

Here are 5 related questions you may find helpful:
1. How do you calculate the volume of a general tetrahedron?
2. What are the properties of a right tetrahedron?
3. How is the volume of a pyramid related to the volume of a tetrahedron?
4. How can you use vectors to find the volume of a tetrahedron?
5. How do you find the surface area of a tetrahedron?

**Tip:** Always make sure that the units for all dimensions are consistent before calculating volume or area in any problem!

Find the volume of the given right tetrahedron. (Hint: Consider slices perpendicular to one of the labeled edges.)

Learn how to calculate the volume of a right tetrahedron using labeled edges. This solution demonstrates the use of geometry concepts, including the base area of a triangle and the volume formula for pyramids and tetrahedrons. Suitable for students in Grades 9-12.

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