Width of Large Rectangle of Skewed Cuboid given First Medium Diagonal Calculator

Formula Used:

\[ w_{Large} = \sqrt{d_{1(Medium)}^2 - l_{Small}^2 - h^2} \]

First Medium Diagonal of Skewed Cuboid:

Length of Small Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Width of Large Rectangle of Skewed Cuboid:

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

The Width of Large Rectangle of Skewed Cuboid given First Medium Diagonal is the length of the shorter edge of the larger rectangular base surface of Skewed Cuboid, calculated using the first medium diagonal, length of small rectangle, and height of the skewed cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ w_{Large} = \sqrt{d_{1(Medium)}^2 - l_{Small}^2 - h^2} \]

Where:

\( w_{Large} \) — Width of Large Rectangle of Skewed Cuboid (m)
\( d_{1(Medium)} \) — First Medium Diagonal of Skewed Cuboid (m)
\( l_{Small} \) — 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-dimensional space to calculate the width component from the given diagonal and other dimensions.

3. Importance of Width Calculation

Details: Calculating the width of the large rectangle is essential for determining the complete dimensional properties of a skewed cuboid, which is important in various engineering, architectural, and geometric applications.

4. Using the Calculator

Tips: Enter the first medium diagonal, length of small rectangle, and height in meters. All values must be positive numbers greater than zero for accurate calculation.

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 to calculate the length of one side of a right triangle when the hypotenuse and other sides are known, following the Pythagorean theorem.

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

Q4: Can this formula be used for any type of cuboid?
A: This specific formula is designed for skewed cuboids where the base and top rectangles have different dimensions and are not parallel.

Q5: What if I get a negative value inside the square root?
A: A negative value inside the square root indicates that the input values do not form a valid skewed cuboid with the given dimensions. Please verify your input values.