Short Width of Rectangular Hexagon Given Perimeter, Diagonal, Inner Length and Width Calculator

Formula Used:

\[ \text{Short Width} = \sqrt{\text{Diagonal}^2 - \left(\frac{\text{Perimeter}}{2} - \text{Width} - \text{Inner Length}\right)^2} \]

Diagonal of Rectangular Hexagon:

Perimeter of Rectangular Hexagon:

Width of Rectangular Hexagon:

Inner Length of Rectangular Hexagon:

Short Width of Rectangular Hexagon:

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1. What is Short Width of Rectangular Hexagon?

The Short Width of Rectangular Hexagon is the remaining length of the rectangle width from which the Rectangular Hexagon shape forms, after removing the cut rectangular portion. It represents the shorter dimension of the hexagon's cross-section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Short Width} = \sqrt{\text{Diagonal}^2 - \left(\frac{\text{Perimeter}}{2} - \text{Width} - \text{Inner Length}\right)^2} \]

Where:

Diagonal — Distance between the inner vertex and the vertex opposite to it (m)
Perimeter — Sum of all the sides of the Rectangular Hexagon (m)
Width — Length of shortest side of the original rectangle (m)
Inner Length — Length of the inner edge parallel to the length (m)

Explanation: This formula calculates the short width using geometric relationships between the diagonal, perimeter, width, and inner length of a rectangular hexagon.

3. Importance of Short Width Calculation

Details: Calculating the short width is essential for determining the complete geometric properties of rectangular hexagons, which are important in various engineering and architectural applications where hexagonal shapes are used.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure all values are positive and the expression inside the square root is non-negative for valid results. The calculator provides precise results up to 6 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rectangular Hexagon?
A: A rectangular hexagon is a six-sided polygon formed by cutting smaller rectangles from the corners of a larger rectangle, creating a shape with both rectangular and hexagonal properties.

Q2: When is this calculation most useful?
A: This calculation is particularly useful in construction, manufacturing, and design applications where precise dimensional calculations of hexagonal structures are required.

Q3: What if I get a negative value under the square root?
A: A negative value under the square root indicates that the input values are inconsistent and cannot form a valid rectangular hexagon. Please verify your measurements.

Q4: Can this formula be used for any rectangular hexagon?
A: This formula applies specifically to rectangular hexagons where the cut portions are rectangular and the remaining shape maintains specific geometric relationships.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input values, with rounding to 6 decimal places for practical use.