Perimeter of Parallelepiped given Lateral Surface Area, Total Surface Area, Side B and Side C Calculator

Formula Used:

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

Total Surface Area of Parallelepiped (TSA):

m²

Lateral Surface Area of Parallelepiped (LSA):

m²

Side C of Parallelepiped (S_c):

Angle Beta of Parallelepiped (β):

Side B of Parallelepiped (S_b):

Perimeter of Parallelepiped (P):

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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:

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

Where:

\( P \) — Perimeter of Parallelepiped (m)
\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( S_c \) — Side C of Parallelepiped (m)
\( \beta \) — Angle Beta of Parallelepiped (degrees)
\( S_b \) — Side B of Parallelepiped (m)

Explanation: This formula calculates the perimeter by utilizing the relationship between surface areas, side lengths, and the angle between sides 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 values in appropriate units (meters for lengths, square meters for areas, degrees for angles). All values must be positive numbers.

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: Why is the sine function used in the formula?
A: The sine function accounts for the angular relationship between the sides of the parallelepiped, which affects the surface area calculations.

Q3: What's the difference between total surface area and lateral surface area?
A: Total surface area includes all six faces, while lateral surface area excludes the top and bottom faces.

Q4: Can this formula be used for any parallelepiped?
A: Yes, this formula applies to all parallelepipeds, including rectangular boxes and oblique parallelepipeds.

Q5: What if I have measurements in different units?
A: Convert all measurements to consistent units (meters and square meters) before using the calculator for accurate results.