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

Total Surface Area Of Parallelepiped Formula:

\[ TSA = 2 \times \left( \left( \left( \frac{P}{4} - S_b - S_c \right) \times S_b \times \sin(\gamma) \right) + \left( \left( \frac{P}{4} - S_b - S_c \right) \times S_c \times \sin(\beta) \right) + \left( S_b \times S_c \times \sin(\alpha) \right) \right) \]

Perimeter of Parallelepiped (P):

Side B of Parallelepiped (S_b):

Side C of Parallelepiped (S_c):

Angle Gamma (γ):

Angle Beta (β):

Angle Alpha (α):

Total Surface Area (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Surface Area of Parallelepiped?

The Total Surface Area (TSA) of a parallelepiped is the total area of all its six faces. A parallelepiped is a three-dimensional figure formed by six parallelograms. The formula calculates the sum of areas of all faces using the perimeter and two sides along with the angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( P \) — Perimeter of the parallelepiped
\( S_b \) — Length of side B
\( S_c \) — Length of side C
\( \gamma \) — Angle between sides A and B
\( \beta \) — Angle between sides A and C
\( \alpha \) — Angle between sides B and C

Explanation: The formula calculates the area of each pair of opposite faces and sums them up to get the total surface area.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important in various fields including architecture, engineering, and manufacturing. It helps in determining the amount of material needed to construct or cover a parallelepiped-shaped object.

4. Using the Calculator

Tips: Enter the perimeter in meters, side lengths in meters, and angles in degrees. All values must be positive numbers. The calculated side A (P/4 - S_b - S_c) must also be positive for valid results.

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 is the perimeter divided by 4 in the formula?
A: In a parallelepiped, the perimeter is the sum of all edges. Since there are 4 edges of each type (A, B, and C), dividing by 4 gives the sum of one edge of each type (A + B + C).

Q3: What are the angle ranges for valid inputs?
A: All angles should be between 0° and 180° (exclusive) for the formula to be valid. Angles of 0° or 180° would represent degenerate cases.

Q4: Can this calculator handle different units?
A: The calculator assumes consistent units for all length measurements. You can use any unit (cm, m, inches, etc.) as long as all length inputs use the same unit.

Q5: What if I get a negative result for side A?
A: A negative result for side A indicates that the input values are inconsistent with a valid parallelepiped. Please verify your inputs for perimeter, side B, and side C.