Breadth of Concave Regular Hexagon given Height Calculator

Formula Used:

\[ b = \frac{2}{\sqrt{3}} \times h \]

Breadth of Concave Regular Hexagon:

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1. What is the Breadth of Concave Regular Hexagon?

The Breadth of Concave Regular Hexagon is the perpendicular distance from the left most point to the right most point of the Concave Regular Hexagon. It is an important geometric measurement used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{2}{\sqrt{3}} \times h \]

Where:

\( b \) — Breadth of Concave Regular Hexagon (m)
\( h \) — Height of Concave Regular Hexagon (m)

Explanation: This formula establishes the mathematical relationship between the height and breadth of a concave regular hexagon, using the square root function to maintain geometric proportionality.

3. Importance of Breadth Calculation

Details: Accurate breadth calculation is crucial for geometric analysis, architectural design, and engineering applications involving hexagonal structures. It helps in determining the spatial requirements and dimensional relationships in concave hexagonal shapes.

4. Using the Calculator

Tips: Enter the height of the concave regular hexagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a concave regular hexagon?
A: A concave regular hexagon is a six-sided polygon with equal sides and angles, but with at least one interior angle greater than 180 degrees, causing the shape to "cave in" at certain points.

Q2: Why is the square root of 3 used in the formula?
A: The square root of 3 appears due to the trigonometric relationships in equilateral triangles that form the basis of hexagonal geometry, specifically from the 30-60-90 triangle ratios.

Q3: Can this formula be used for convex hexagons?
A: No, this specific formula applies only to concave regular hexagons. Convex hexagons have different geometric properties and require different calculation methods.

Q4: What are the units of measurement?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as both height and breadth use the same units.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric properties of concave regular hexagons. The accuracy depends on the precision of the input height value.