Total Surface Area of Parallelepiped given Lateral Surface Area Calculator

Formula Used:

\[ TSA = LSA + 2 \times S_a \times S_c \times \sin(\beta) \]

Lateral Surface Area of Parallelepiped:

m²

Side A of Parallelepiped:

Side C of Parallelepiped:

Angle Beta 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 includes all six faces of the three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = LSA + 2 \times S_a \times S_c \times \sin(\beta) \]

Where:

\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( S_a \) — Side A of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \beta \) — Angle Beta of Parallelepiped (°)

Explanation: The formula calculates the total surface area by adding the lateral surface area to twice the product of side A, side C, and the sine of angle beta.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, packaging design, structural analysis, and geometric modeling of three-dimensional objects.

4. Using the Calculator

Tips: Enter lateral surface area in m², side lengths in meters, and angle beta in degrees. All values must be positive (side lengths > 0, angle between 0-180°).

5. Frequently Asked Questions (FAQ)

Q1: What is a Parallelepiped?
A: A Parallelepiped is a three-dimensional figure formed by six parallelograms. It's a polyhedron with parallelogram faces.

Q2: How is Lateral Surface Area different from Total Surface Area?
A: Lateral Surface Area excludes the top and bottom faces, while Total Surface Area includes all six faces of the Parallelepiped.

Q3: What is Angle Beta in a Parallelepiped?
A: Angle Beta is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

Q4: Can this formula be used for all types of Parallelepipeds?
A: Yes, this formula applies to all parallelepipeds regardless of whether they are rectangular or oblique.

Q5: What units should be used for the inputs?
A: Use consistent units - typically meters for lengths and square meters for areas. The angle should be in degrees.