Total Surface Area Of Parallelepiped Given Perimeter, Side A And Side B Calculator

Formula Used:

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

Side A of Parallelepiped:

Side B of Parallelepiped:

Perimeter 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. It represents the sum of the areas of all six faces of this three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( S_a \) — Side A of Parallelepiped (m)
\( S_b \) — Side B of Parallelepiped (m)
\( P \) — Perimeter of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (radians)
\( \beta \) — Angle Beta of Parallelepiped (radians)
\( \gamma \) — Angle Gamma of Parallelepiped (radians)

Explanation: The formula calculates the surface area by summing the areas of all six faces, which are arranged in three pairs of opposite faces with equal areas.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation for construction, packaging design, heat transfer calculations, and determining coating/painting requirements for three-dimensional objects.

4. Using the Calculator

Tips: Enter all side lengths in meters, perimeter in meters, and angles in degrees. All values must be positive numbers. Side C is automatically calculated as (Perimeter/4 - Side A - Side B).

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's the 3D equivalent of a parallelogram.

Q2: How is the perimeter related to the sides?
A: The perimeter of a parallelepiped is calculated as P = 4 × (S_a + S_b + S_c), where S_c is the third side.

Q3: What are the angle ranges for a valid parallelepiped?
A: All angles should be between 0° and 180°, and the sum of angles around any vertex should be less than 360° for a valid parallelepiped.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length units, but you can use any consistent unit system as long as all length measurements are in the same units.

Q5: What if I get negative results for side C?
A: A negative result for side C indicates that the input values don't form a valid parallelepiped. Please check your perimeter and side measurements.