Length of Small Rectangle of Skewed Cuboid given Short Diagonal Calculator

Formula Used:

\[ lSmall = \sqrt{dShort^2 - wSmall^2 - h^2} \]

Short Diagonal of Skewed Cuboid (dShort):

Width of Small Rectangle of Skewed Cuboid (wSmall):

Height of Skewed Cuboid (h):

Length of Small Rectangle of Skewed Cuboid (lSmall):

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1. What is the Length of Small Rectangle of Skewed Cuboid given Short Diagonal?

The Length of Small Rectangle of Skewed Cuboid given Short Diagonal calculates the length of the longer edge of the smaller rectangular top surface face of Skewed Cuboid using the short diagonal, width of small rectangle, and height of the skewed cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ lSmall = \sqrt{dShort^2 - wSmall^2 - h^2} \]

Where:

\( lSmall \) — Length of Small Rectangle of Skewed Cuboid (m)
\( dShort \) — Short Diagonal of Skewed Cuboid (m)
\( wSmall \) — Width of Small 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 short diagonal forms the hypotenuse of a right triangle with the length, width, and height as the other sides.

3. Importance of Length Calculation

Details: Calculating the length of the small rectangle is essential for determining the complete geometric properties of a skewed cuboid, which is important in various engineering, architectural, and mathematical applications involving three-dimensional shapes.

4. Using the Calculator

Tips: Enter the short diagonal, width of small rectangle, and height in meters. All values must be positive numbers. The calculator will compute the length using the square root function.

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 rather than rectangles.

Q2: Why is the square root function used in this formula?
A: The square root function is used to solve for the length component from the three-dimensional Pythagorean relationship between the diagonal and the three perpendicular dimensions.

Q3: What units should be used for input values?
A: All input values should be in consistent units (preferably meters) as the formula is dimensionally consistent.

Q4: Are there any limitations to this calculation?
A: The formula assumes the input values form a valid geometric configuration where dShort² > wSmall² + h² to avoid negative values under the square root.

Q5: Can this formula be used for other types of cuboids?
A: This specific formula applies to skewed cuboids where the top and bottom rectangles are of different sizes. For regular cuboids, simpler formulas apply.