Width of Small Rectangle of Skewed Cuboid given Second Medium Diagonal Calculator

Formula Used:

\[ wSmall = \sqrt{d2(Medium)^2 - lLarge^2 - h^2} \]

Second Medium Diagonal of Skewed Cuboid:

Length of Large Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Width of Small Rectangle of Skewed Cuboid:

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1. What is the Width of Small Rectangle of Skewed Cuboid given Second Medium Diagonal?

The Width of Small Rectangle of Skewed Cuboid given Second Medium Diagonal is the length of the shorter edge of the smaller rectangular top surface of a Skewed Cuboid, calculated using the second medium diagonal, length of large rectangle, and height of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ wSmall = \sqrt{d2(Medium)^2 - lLarge^2 - h^2} \]

Where:

\( wSmall \) — Width of Small Rectangle of Skewed Cuboid (m)
\( d2(Medium) \) — Second Medium Diagonal of Skewed Cuboid (m)
\( lLarge \) — Length of Large Rectangle of Skewed Cuboid (m)
\( h \) — Height of Skewed Cuboid (m)

Explanation: This formula uses the Pythagorean theorem in three dimensions to calculate the width of the small rectangle based on the given diagonal and other dimensions.

3. Importance of Width Calculation

Details: Calculating the width of the small rectangle is essential for understanding the geometry of skewed cuboids, which is important in various engineering and architectural applications where non-rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the second medium diagonal, length of large rectangle, and height of the skewed cuboid in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the square root function used in this formula?
A: The square root function is used because the formula is derived from the three-dimensional Pythagorean theorem, which involves calculating distances in 3D space.

Q3: What are the units of measurement for this calculation?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit of length (cm, mm, inches, etc.).

Q4: Can this formula be used for any type of cuboid?
A: This specific formula is designed for skewed cuboids where the top and bottom rectangles have different dimensions and are offset from each other.

Q5: What if the result is imaginary (negative under square root)?
A: An imaginary result indicates that the input values do not form a valid skewed cuboid geometry. Please check your input values.