Area of Rectangular Hexagon given Diagonal, Inner Length, Inner Width and Short Width Calculator

Area of Rectangular Hexagon Formula:

\[ A = ((\sqrt{d^2 - w_{Short}^2}) + l_{Inner}) \times (w_{Short} + w_{Inner}) - (l_{Inner} \times w_{Inner}) \]

Diagonal of Rectangular Hexagon:

Short Width of Rectangular Hexagon:

Inner Length of Rectangular Hexagon:

Inner Width of Rectangular Hexagon:

Area of Rectangular Hexagon:

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1. What is the Area of Rectangular Hexagon?

The Area of Rectangular Hexagon is the amount of 2-dimensional space covered or occupied by the figure. It is calculated using specific dimensions including diagonal, short width, inner length, and inner width.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = ((\sqrt{d^2 - w_{Short}^2}) + l_{Inner}) \times (w_{Short} + w_{Inner}) - (l_{Inner} \times w_{Inner}) \]

Where:

\( A \) — Area of Rectangular Hexagon (m²)
\( d \) — Diagonal of Rectangular Hexagon (m)
\( w_{Short} \) — Short Width of Rectangular Hexagon (m)
\( l_{Inner} \) — Inner Length of Rectangular Hexagon (m)
\( w_{Inner} \) — Inner Width of Rectangular Hexagon (m)

Explanation: The formula calculates the area by first finding the missing dimension using the Pythagorean theorem, then computing the total area and subtracting the inner rectangular portion.

3. Importance of Area Calculation

Details: Calculating the area of a rectangular hexagon is important in various fields including architecture, engineering, and manufacturing where this shape is commonly used in design and construction.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure the diagonal is greater than the short width for valid calculation. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rectangular Hexagon?
A: A rectangular hexagon is a six-sided polygon formed by removing a smaller rectangle from a larger rectangle, creating a shape with both inner and outer dimensions.

Q2: Why is the diagonal measurement important?
A: The diagonal helps determine the missing dimension of the shape using the Pythagorean theorem, which is essential for calculating the total area.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert all measurements to meters before calculation.

Q4: What if the diagonal is smaller than the short width?
A: The calculation requires that the diagonal be greater than the short width. Otherwise, the square root operation would result in an imaginary number.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The result is rounded to 6 decimal places for practical use.