Length of Large Rectangle of Skewed Cuboid given Second Medium Diagonal Calculator

Formula Used:

\[ l_{Large} = \sqrt{d_{2(Medium)}^2 - w_{Small}^2 - h^2} \]

Second Medium Diagonal of Skewed Cuboid (d₂(Medium)):

Width of Small Rectangle of Skewed Cuboid (w_Small):

Height of Skewed Cuboid (h):

Length of Large Rectangle of Skewed Cuboid (l_Large):

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1. What is the Length of Large Rectangle of Skewed Cuboid given Second Medium Diagonal?

The Length of Large Rectangle of Skewed Cuboid given Second Medium Diagonal is the length of the longer edge of the larger rectangular base surface of a Skewed Cuboid, calculated using the second medium diagonal, width of the small rectangle, and height of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Large} = \sqrt{d_{2(Medium)}^2 - w_{Small}^2 - h^2} \]

Where:

\( l_{Large} \) — Length of Large Rectangle of Skewed Cuboid (m)
\( d_{2(Medium)} \) — Second Medium Diagonal of Skewed Cuboid (m)
\( w_{Small} \) — Width of Small Rectangle of Skewed Cuboid (m)
\( h \) — Height of Skewed Cuboid (m)

Explanation: This formula derives from the Pythagorean theorem applied in three-dimensional space, relating the diagonal to the three perpendicular dimensions of the skewed cuboid.

3. Importance of Length Calculation

Details: Calculating the length of the large rectangle is essential for determining the complete dimensions of a skewed cuboid, which is crucial in various engineering, architectural, and geometric applications where precise measurements are required.

4. Using the Calculator

Tips: Enter the second medium diagonal, width of the small rectangle, and height of the skewed cuboid in meters. All values must be valid and positive numbers. The calculator will compute the length of the large rectangle using the mathematical formula.

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 rather than rectangles.

Q2: Why is this calculation important?
A: This calculation helps determine one of the fundamental dimensions of a skewed cuboid, which is essential for volume calculation, surface area determination, and structural analysis.

Q3: What units should I use?
A: The calculator uses meters (m) as the default unit, but the formula works with any consistent unit of measurement.

Q4: Are there any limitations to this formula?
A: The formula assumes the input values form a valid geometric configuration where the square root operation yields a real number result.

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