Side C of Parallelepiped given Total Surface Area and Lateral Surface Area Calculator

Formula Used:

\[ S_c = \frac{TSA - LSA}{2 \times S_a \times \sin(\angle\beta)} \]

Total Surface Area of Parallelepiped:

m²

Lateral Surface Area of Parallelepiped:

m²

Side A of Parallelepiped:

Angle Beta of Parallelepiped:

Side C of Parallelepiped:

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1. What is the Side C of Parallelepiped Calculation?

The Side C of Parallelepiped calculation determines the length of one of the three sides of a parallelepiped using the total surface area, lateral surface area, side A, and angle beta. This geometric calculation is essential in 3D geometry and spatial analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S_c = \frac{TSA - LSA}{2 \times S_a \times \sin(\angle\beta)} \]

Where:

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

Explanation: The formula calculates side C by finding the difference between total and lateral surface areas, then dividing by twice the product of side A and the sine of angle beta.

3. Importance of Side C Calculation

Details: Calculating side C is crucial for determining the complete dimensions of a parallelepiped, which is essential in architecture, engineering, and 3D modeling applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, square meters for areas, degrees for angles). Ensure all values are positive and angle beta is between 0-180 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 a polyhedron with parallelogram faces.

Q2: Why is angle beta important in this calculation?
A: Angle beta determines the relationship between side A and side C, affecting the surface area distribution and thus the calculation of side C.

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

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

Q5: What if I get a negative result?
A: A negative result indicates invalid input values, as lengths and areas cannot be negative. Check your input values for accuracy.