Total Surface Area Of Parallelepiped Calculator

Formula Used:

\[ TSA = 2 \times ((S_a \times S_b \times \sin(\gamma)) + (S_a \times S_c \times \sin(\beta)) + (S_b \times S_c \times \sin(\alpha))) \]

Side A of Parallelepiped:

Side B of Parallelepiped:

Side C of Parallelepiped:

Angle Alpha of Parallelepiped:

Angle Beta of Parallelepiped:

Angle Gamma of Parallelepiped:

Total Surface Area of Parallelepiped:

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1. What is the Total Surface Area of Parallelepiped?

The Total Surface Area of a Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped. A parallelepiped is a three-dimensional figure formed by six parallelograms.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times ((S_a \times S_b \times \sin(\gamma)) + (S_a \times S_c \times \sin(\beta)) + (S_b \times S_c \times \sin(\alpha))) \]

Where:

\( S_a \) — Side A of Parallelepiped (m)
\( S_b \) — Side B of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (degrees)
\( \beta \) — Angle Beta of Parallelepiped (degrees)
\( \gamma \) — Angle Gamma of Parallelepiped (degrees)

Explanation: The formula calculates the sum of the areas of all six faces of the parallelepiped, accounting for the angles between the sides.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is important in various fields including architecture, engineering, and manufacturing for determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter all three side lengths in meters and all three angles in degrees. All values must be positive numbers, with angles between 0-180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure with six faces, each of which is a parallelogram. It's the 3D analog of a parallelogram.

Q2: How is this different from a rectangular prism?
A: A rectangular prism is a special case of a parallelepiped where all angles are 90 degrees. The general parallelepiped can have angles other than 90 degrees.

Q3: What are the units of measurement?
A: Side lengths should be in meters (or consistent units), angles in degrees, and the resulting surface area will be in square meters (or square units of the input).

Q4: Can angles be greater than 180 degrees?
A: No, the angles between sides in a parallelepiped must be between 0 and 180 degrees, exclusive.

Q5: What if I have obtuse angles?
A: The formula works for both acute and obtuse angles, as the sine function handles angles up to 180 degrees correctly.