Width Of Small Rectangle Of Skewed Cuboid Given Short Diagonal Calculator

Formula Used:

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

Short Diagonal of Skewed Cuboid:

Length of Small 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 Short Diagonal?

The Width of Small Rectangle of Skewed Cuboid given Short Diagonal is the length of the shorter edge of the smaller rectangular top surface of a Skewed Cuboid, calculated using the short diagonal, length of the small rectangle, and height of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

3. Importance of Width Calculation

Details: Calculating the width of the small rectangle is essential for determining the geometric properties of a skewed cuboid, which is important in various engineering, architectural, and mathematical applications involving 3D shapes.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: The calculator expects all inputs in meters (m) for consistency. Make sure to convert other units to meters before calculation.

Q2: What if I get a negative value inside the square root?
A: A negative value indicates that the input values do not form a valid skewed cuboid. Please check your measurements and ensure they satisfy the triangle inequality in three dimensions.

Q3: Can this formula be used for any type of cuboid?
A: This specific formula is designed for skewed cuboids where the top and bottom faces are rectangles of different sizes and are not parallel.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the Pythagorean theorem. The accuracy depends on the precision of your input measurements.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering, 3D modeling, and any field that involves working with irregular 3D shapes and spatial measurements.