Length Of Large Rectangle Of Skewed Cuboid Given Long Diagonal Calculator

Formula Used:

\[ l_{Large} = \sqrt{d_{Long}^2 - w_{Large}^2 - h^2} \]

Long Diagonal of Skewed Cuboid:

Width of Large Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Length of Large Rectangle of Skewed Cuboid:

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1. What is Length of Large Rectangle of Skewed Cuboid given Long Diagonal?

The Length of Large Rectangle of Skewed Cuboid given Long Diagonal is the length of the longer edge of the larger rectangular base surface of Skewed Cuboid, calculated using the long diagonal, width of the large rectangle, and height of the skewed cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Large} = \sqrt{d_{Long}^2 - w_{Large}^2 - h^2} \]

Where:

\( l_{Large} \) — Length of Large Rectangle of Skewed Cuboid (m)
\( d_{Long} \) — Long Diagonal of Skewed Cuboid (m)
\( w_{Large} \) — Width of Large Rectangle of Skewed Cuboid (m)
\( h \) — Height of Skewed Cuboid (m)

Explanation: This formula applies the Pythagorean theorem in three dimensions to calculate the length of the large rectangle from the given diagonal and other dimensions.

3. Importance of Length Calculation

Details: Accurate calculation of the length of the large rectangle is essential for determining the complete geometric properties of a skewed cuboid, which is important in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter the long diagonal, width of large rectangle, and height in meters. All values must be positive numbers. The calculator will compute the length of the large rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What is a skewed cuboid?
A: A skewed cuboid is a three-dimensional shape where the base and top are rectangles of different sizes, and the lateral faces are parallelograms.

Q2: Why is this calculation important?
A: This calculation helps determine the complete dimensions of a skewed cuboid, which is useful in construction, manufacturing, and geometric modeling.

Q3: What units should I use?
A: The calculator uses meters (m) as the default unit, but you can use any consistent unit of length as long as all inputs are in the same unit.

Q4: Are there any limitations to this formula?
A: The formula assumes that the given dimensions form a valid skewed cuboid and that the long diagonal is indeed the longest diagonal of the shape.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs with up to 4 decimal places for precise calculations.