Third Right Angle Edge Of Trirectangular Tetrahedron Given Total Surface Area Calculator

Formula Used:

\[ Third\ RA\ Edge = \frac{(2 \times Total\ Surface\ Area) - (First\ RA\ Edge \times Second\ RA\ Edge)}{First\ RA\ Edge + Second\ RA\ Edge + \frac{First\ RA\ Edge \times Second\ RA\ Edge}{Height}} \]

Total Surface Area (TSA):

m²

First RA Edge:

Second RA Edge:

Height:

Third RA Edge:

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1. What is the Third RA Edge of Trirectangular Tetrahedron?

The Third RA Edge of a Trirectangular Tetrahedron is the third edge out of the three mutually perpendicular edges of the Trirectangular Tetrahedron. It completes the set of right-angle edges that define the tetrahedron's geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Third\ RA\ Edge = \frac{(2 \times Total\ Surface\ Area) - (First\ RA\ Edge \times Second\ RA\ Edge)}{First\ RA\ Edge + Second\ RA\ Edge + \frac{First\ RA\ Edge \times Second\ RA\ Edge}{Height}} \]

Where:

Total Surface Area (TSA) — Total surface area of the trirectangular tetrahedron (m²)
First RA Edge — First right-angle edge of the tetrahedron (m)
Second RA Edge — Second right-angle edge of the tetrahedron (m)
Height — Height of the trirectangular tetrahedron (m)

Explanation: This formula calculates the third right-angle edge when the total surface area and the other two right-angle edges are known, incorporating the height parameter for accurate computation.

3. Importance of Calculating the Third RA Edge

Details: Determining the third right-angle edge is essential for complete geometric characterization of trirectangular tetrahedra, which is important in various fields including crystallography, architectural design, and 3D modeling.

4. Using the Calculator

Tips: Enter all values in meters and square meters. Ensure all values are positive and non-zero for accurate results. The calculator provides the third right-angle edge measurement in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a trirectangular tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces that are mutually perpendicular right triangles meeting at a vertex.

Q2: Why is the height parameter needed in this calculation?
A: The height is necessary to account for the three-dimensional geometry and the relationship between the edges and surface area of the tetrahedron.

Q3: Can this formula be used for any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedra where three edges are mutually perpendicular.

Q4: What are practical applications of this calculation?
A: This calculation is useful in structural engineering, 3D computer graphics, crystallography, and any field dealing with spatial geometry analysis.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal trirectangular tetrahedra when all input values are precise.