Width of Large Rectangle of Skewed Cuboid given Long Diagonal Calculator

Formula Used:

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

Long Diagonal of Skewed Cuboid:

Length of Large Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Width of Large Rectangle of Skewed Cuboid:

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Width of Large Rectangle of Skewed Cuboid given Long Diagonal is the length of the shorter edge of the larger rectangular base surface of a Skewed Cuboid, calculated using the long diagonal and other dimensions of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula is derived from the Pythagorean theorem applied in three-dimensional space, where the long diagonal serves as the hypotenuse of a right-angled triangle formed by the length, width, and height dimensions.

3. Importance of Width Calculation

Details: Calculating the width 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 long diagonal, length of large rectangle, and height in meters. All values must be positive numbers. The calculator will compute the width using the geometric relationship between these dimensions.

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 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, where the diagonal squared equals the sum of the squares of the three perpendicular dimensions.

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

Q4: What if the result under the square root is negative?
A: If the result under the square root is negative, it indicates that the input values do not form a valid skewed cuboid with the given dimensions. Please verify your inputs.

Q5: Can this calculator be used for other geometric shapes?
A: No, this specific formula and calculator are designed specifically for calculating the width of the large rectangle in a skewed cuboid given its long diagonal and other dimensions.