Perimeter of Parallelepiped given Volume, Side A and Side B Calculator

Perimeter of Parallelepiped Formula:

\[ P = 4 \times \left( Sa + Sb + \frac{V}{Sb \times Sa \times \sqrt{1 + (2 \times \cos(\angle\alpha) \times \cos(\angle\beta) \times \cos(\angle\gamma)) - (\cos(\angle\alpha)^2 + \cos(\angle\beta)^2 + \cos(\angle\gamma)^2)}} \right) \]

Side A of Parallelepiped:

Side B of Parallelepiped:

Volume of Parallelepiped:

m³

Angle Alpha of Parallelepiped:

rad

Angle Beta of Parallelepiped:

rad

Angle Gamma of Parallelepiped:

rad

Perimeter of Parallelepiped:

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1. What is the Perimeter of Parallelepiped?

The perimeter of a parallelepiped is the total distance around the edge of the three-dimensional geometric shape. It represents the sum of all the edges of the parallelepiped.

2. How Does the Calculator Work?

The calculator uses the perimeter formula:

Where:

\( P \) — Perimeter of Parallelepiped (m)
\( Sa \) — Side A of Parallelepiped (m)
\( Sb \) — Side B of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( \angle\alpha \) — Angle Alpha of Parallelepiped (rad)
\( \angle\beta \) — Angle Beta of Parallelepiped (rad)
\( \angle\gamma \) — Angle Gamma of Parallelepiped (rad)

Explanation: The formula calculates the perimeter based on two sides, volume, and the three angles between the sides, accounting for the geometric relationships in a parallelepiped.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a parallelepiped is important in various engineering, architectural, and geometric applications where the boundary measurement of three-dimensional objects is required.

4. Using the Calculator

Tips: Enter all side lengths in meters, volume in cubic meters, and angles in radians. All values must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It has 8 vertices, 12 edges, and 6 faces.

Q2: Why are three angles needed for the calculation?
A: The three angles (alpha, beta, gamma) define the spatial relationships between the sides of the parallelepiped and are essential for accurate perimeter calculation.

Q3: Can this calculator handle different units?
A: The calculator uses consistent units (meters for length, cubic meters for volume, radians for angles). Convert all inputs to these units before calculation.

Q4: What if I have missing angle values?
A: All three angles are required for this calculation. If angles are unknown, alternative methods or measurements may be needed.

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