Height of Skewed Cuboid given Left Skewed Edge Calculator

Formula Used:

\[ h = \sqrt{le_{Left\ Skewed}^2 - (w_{Large} - w_{Small})^2} \]

Left Skewed Edge of Skewed Cuboid:

Width of Large Rectangle of Skewed Cuboid:

Width of Small Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Height of Skewed Cuboid given Left Skewed Edge?

The Height of Skewed Cuboid given Left Skewed Edge is the vertical distance measured from base to the top of Skewed Cuboid, calculated using the left skewed edge and the difference between the widths of the large and small rectangles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{le_{Left\ Skewed}^2 - (w_{Large} - w_{Small})^2} \]

Where:

\( h \) — Height of Skewed Cuboid (m)
\( le_{Left\ Skewed} \) — Left Skewed Edge of Skewed Cuboid (m)
\( w_{Large} \) — Width of Large Rectangle of Skewed Cuboid (m)
\( w_{Small} \) — Width of Small Rectangle of Skewed Cuboid (m)

Explanation: This formula applies the Pythagorean theorem to calculate the height of the skewed cuboid using the given edge lengths and width differences.

3. Importance of Height Calculation

Details: Accurate height calculation is crucial for determining the volume, surface area, and other geometric properties of skewed cuboids in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers. Ensure that the left skewed edge is longer than the difference between the large and small rectangle widths for valid results.

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 side faces are trapezoids rather than rectangles.

Q2: Why is the square root function used in this formula?
A: The square root function is used to calculate the height from the hypotenuse (left skewed edge) and the base difference, following the Pythagorean theorem.

Q3: What units should be used for input values?
A: All input values should be in consistent units (preferably meters) for accurate results. The calculator will output the height in the same units.

Q4: What if the result is imaginary?
A: If the difference between widths is larger than the left skewed edge, the result would be imaginary, indicating invalid input dimensions for a physical skewed cuboid.

Q5: Can this formula be used for right cuboids?
A: For right cuboids (where top and bottom rectangles are identical), the formula simplifies as the width difference becomes zero, making the height equal to the left skewed edge.