Length of Small Rectangle of Skewed Cuboid given First Medium Diagonal Calculator

Formula Used:

\[ lSmall = \sqrt{d1(Medium)^2 - wLarge^2 - h^2} \]

First Medium Diagonal of Skewed Cuboid:

Width of Large Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Length of Small Rectangle of Skewed Cuboid:

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

The Length of Small Rectangle of Skewed Cuboid given First Medium Diagonal is the length of the longer edge of the smaller rectangular top surface face of Skewed Cuboid, calculated using the first medium diagonal, width of large rectangle, and height of the skewed cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ lSmall = \sqrt{d1(Medium)^2 - wLarge^2 - h^2} \]

Where:

\( lSmall \) — Length of Small Rectangle of Skewed Cuboid (m)
\( d1(Medium) \) — First Medium Diagonal of Skewed Cuboid (m)
\( wLarge \) — Width 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 length of the small rectangle from the given diagonal and other dimensions.

3. Importance of Length Calculation

Details: Calculating the length of the small rectangle is essential for determining the complete geometry of a skewed cuboid, which is important in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter the first medium diagonal, width 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 to calculate the length from the squared differences in the three-dimensional Pythagorean theorem.

Q3: What are the units of measurement for this calculation?
A: The calculator uses meters as the unit of measurement, but the formula works with any consistent unit system.

Q4: Can this formula be used for any skewed cuboid?
A: Yes, this formula applies to all skewed cuboids where the given dimensions are known and satisfy the geometric constraints.

Q5: What if the result is imaginary?
A: If the result is imaginary (square root of a negative number), it means the input dimensions are not geometrically possible for a skewed cuboid.