Total Surface Area of Parallelepiped given Perimeter, Side A and Side C Calculator

Total Surface Area of Parallelepiped Formula:

\[ TSA = 2 \times \left( (S_a \times (P/4 - S_a - S_c) \times \sin(\gamma)) + (S_a \times S_c \times \sin(\beta)) + ((P/4 - S_a - S_c) \times S_c \times \sin(\alpha)) \right) \]

Side A of Parallelepiped:

Perimeter of Parallelepiped:

Side C of Parallelepiped:

Angle Gamma (γ):

rad

Angle Beta (β):

rad

Angle Alpha (α):

rad

Total Surface Area of Parallelepiped:

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1. What is 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 three-dimensional figure. A parallelepiped is a three-dimensional figure formed by six parallelograms.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times \left( (S_a \times (P/4 - S_a - S_c) \times \sin(\gamma)) + (S_a \times S_c \times \sin(\beta)) + ((P/4 - S_a - S_c) \times S_c \times \sin(\alpha)) \right) \]

Where:

\( TSA \) — Total Surface Area (m²)
\( S_a \) — Side A of Parallelepiped (m)
\( P \) — Perimeter of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \gamma \) — Angle Gamma between sides (rad)
\( \beta \) — Angle Beta between sides (rad)
\( \alpha \) — Angle Alpha between sides (rad)

Explanation: The formula calculates the sum of areas of all six parallelogram faces that make up the parallelepiped.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, heat transfer calculations, packaging design, and architectural planning involving three-dimensional parallelepiped structures.

4. Using the Calculator

Tips: Enter all dimensions in meters and angles in radians. Ensure all values are positive and the perimeter is sufficiently large to accommodate the given sides (P/4 > S_a + S_c).

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 equivalent of a parallelogram.

Q2: Why use radians for angles?
A: The trigonometric functions in mathematical formulas typically use radians as they provide more natural mathematical properties for calculus and advanced mathematics.

Q3: Can I use degrees instead of radians?
A: You would need to convert degrees to radians first (radians = degrees × π/180) as the formula requires angle values in radians.

Q4: What if P/4 - S_a - S_c is negative?
A: This indicates invalid input as the perimeter must be large enough to accommodate the given sides. The calculation requires positive values for all dimensions.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy depends on the precision of your input measurements.