Total Surface Area of Trirectangular Tetrahedron given Volume, First and Third Right Angle Edge Calculator

Formula Used:

\[ TSA = \frac{le(Right1) \times le(Right3)}{2} + \frac{3 \times V}{le(Right3)} + \frac{3 \times V}{le(Right1)} + \frac{3 \times V}{h} \]

First RA Edge of Trirectangular Tetrahedron:

Third RA Edge of Trirectangular Tetrahedron:

Volume of Trirectangular Tetrahedron:

m³

Height of Trirectangular Tetrahedron:

Total Surface Area of Trirectangular Tetrahedron:

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1. What is Total Surface Area of Trirectangular Tetrahedron?

The Total Surface Area of a Trirectangular Tetrahedron is the total quantity of plane enclosed by the entire surface of the Trirectangular Tetrahedron. It represents the sum of the areas of all four triangular faces of the tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{le(Right1) \times le(Right3)}{2} + \frac{3 \times V}{le(Right3)} + \frac{3 \times V}{le(Right1)} + \frac{3 \times V}{h} \]

Where:

\( le(Right1) \) — First RA Edge of Trirectangular Tetrahedron (m)
\( le(Right3) \) — Third RA Edge of Trirectangular Tetrahedron (m)
\( V \) — Volume of Trirectangular Tetrahedron (m³)
\( h \) — Height of Trirectangular Tetrahedron (m)

Explanation: The formula calculates the total surface area by summing the areas of all four triangular faces of the trirectangular tetrahedron.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is important in various engineering and architectural applications where material requirements, heat transfer, or surface coating calculations are needed for tetrahedral structures.

4. Using the Calculator

Tips: Enter all values in meters for edges and height, and cubic meters for volume. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Trirectangular Tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces meeting at one vertex that are mutually perpendicular to each other.

Q2: Why are there three different edge measurements in the formula?
A: The formula uses the first and third right angle edges along with the height to calculate the surface area of all four triangular faces.

Q3: Can this formula be used for any tetrahedron?
A: No, this specific formula is designed for trirectangular tetrahedrons where three edges are mutually perpendicular.

Q4: What units should I use for input values?
A: All linear measurements should be in meters, and volume should be in cubic meters. The calculator will output surface area in square meters.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given formula. Accuracy depends on the precision of your input measurements.