Perimeter of Parallelepiped Given Lateral Surface Area, Total Surface Area, Side A and Side B Calculator

Formula Used:

\[ P = 4 \times \left( S_a + S_b + \frac{TSA - LSA}{2 \times S_a \times \sin(\angle\beta)} \right) \]

Side A of Parallelepiped:

Side B of Parallelepiped:

Total Surface Area of Parallelepiped:

m²

Lateral Surface Area of Parallelepiped:

m²

Angle Beta of Parallelepiped:

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 formula:

\[ P = 4 \times \left( S_a + S_b + \frac{TSA - LSA}{2 \times S_a \times \sin(\angle\beta)} \right) \]

Where:

\( P \) — Perimeter of Parallelepiped (m)
\( S_a \) — Side A of Parallelepiped (m)
\( S_b \) — Side B of Parallelepiped (m)
\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( \angle\beta \) — Angle Beta of Parallelepiped (°)

Explanation: This formula calculates the perimeter by considering the given sides, surface areas, and the angle between specific sides of the parallelepiped.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a parallelepiped is important in various geometric and engineering applications, including material estimation, structural design, and spatial analysis of three-dimensional objects.

4. Using the Calculator

Tips: Enter all required values in the appropriate units. Side lengths and surface areas must be positive values. The angle beta must be between 0 and 180 degrees.

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 this formula derived?
A: The formula is derived from geometric relationships between the sides, angles, and surface areas of a parallelepiped, using trigonometric functions to account for angular relationships.

Q3: What are the units for the perimeter?
A: The perimeter is measured in meters (m) or any other length unit consistent with the input side lengths.

Q4: Can this calculator handle different units?
A: All inputs must use consistent units. If side lengths are in meters, surface areas must be in square meters.

Q5: What if I get a division by zero error?
A: This occurs when the denominator becomes zero, which happens when sin(∠β) = 0. Make sure the angle is not 0° or 180°.