Height of Skewed Cuboid given Second Medium Diagonal Calculator

Formula Used:

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

Second Medium Diagonal of Skewed Cuboid:

Length of Large Rectangle of Skewed Cuboid:

Width of Small Rectangle of Skewed Cuboid:

Height of Skewed Cuboid:

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1. What is the Height of Skewed Cuboid?

The Height of Skewed Cuboid is the vertical distance measured from base to the top of Skewed Cuboid. It is an important geometric parameter in three-dimensional space calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h \) — Height of Skewed Cuboid (m)
\( d_{2(Medium)} \) — Second Medium Diagonal of Skewed Cuboid (m)
\( l_{Large} \) — Length of Large Rectangle of Skewed Cuboid (m)
\( w_{Small} \) — Width of Small Rectangle of Skewed Cuboid (m)

Explanation: This formula calculates the height by applying the Pythagorean theorem in three dimensions, using the relationship between the diagonal and the three perpendicular dimensions.

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 architectural, engineering, and mathematical applications.

4. Using the Calculator

Tips: Enter all three values in meters. Ensure that the second medium diagonal is greater than the square root of the sum of squares of the other two dimensions 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 lateral faces are parallelograms.

Q2: Why is this formula used?
A: This formula applies the three-dimensional Pythagorean theorem to calculate the height when the diagonal and two base dimensions are known.

Q3: What units should be used?
A: All measurements should be in consistent units (meters are recommended). The result will be in the same unit.

Q4: What if I get an imaginary number result?
A: An imaginary result indicates that the input values are inconsistent with a real skewed cuboid. Check that the diagonal is sufficiently large relative to the base dimensions.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs with up to 4 decimal places precision for accurate calculations.