Total Surface Area Of Rhombohedron Given Obtuse Angle Calculator

Formula Used:

\[ TSA = 6 \times l_e^2 \times \sin(\pi - \angle_{Obtuse}) \]

Total Surface Area of Rhombohedron:

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1. What is the Total Surface Area of Rhombohedron?

The Total Surface Area of a Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron. A rhombohedron is a three-dimensional figure with six rhombus-shaped faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 6 \times l_e^2 \times \sin(\pi - \angle_{Obtuse}) \]

Where:

\( TSA \) — Total Surface Area of Rhombohedron (m²)
\( l_e \) — Edge Length of Rhombohedron (m)
\( \angle_{Obtuse} \) — Obtuse Angle of Rhombohedron (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the total surface area by considering the area of all six rhombus faces, each with area \( l_e^2 \times \sin(\pi - \angle_{Obtuse}) \).

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is important in geometry, material science, and engineering applications where the surface properties of rhombohedral structures need to be determined for coating, painting, or material usage calculations.

4. Using the Calculator

Tips: Enter the edge length in meters and the obtuse angle in degrees (between 90 and 180). All values must be valid positive numbers with the angle in the specified range.

5. Frequently Asked Questions (FAQ)

Q1: What is a rhombohedron?
A: A rhombohedron is a three-dimensional figure with six congruent rhombus-shaped faces, where opposite faces are parallel to each other.

Q2: Why is the obtuse angle used in the formula?
A: The obtuse angle is one of the two angles of the rhombus faces, and it's used to calculate the area of each face through the sine function.

Q3: What are typical applications of rhombohedron surface area calculations?
A: These calculations are used in crystallography, material science, architecture, and any field dealing with rhombic structures.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length units, but you can convert other units to meters before inputting the values.

Q5: What if I have the acute angle instead of the obtuse angle?
A: Since the sum of angles in a rhombus is 360° and opposite angles are equal, you can calculate the obtuse angle if you know the acute angle.