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Height of Dodecagon Formula:
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The height of a regular dodecagon (12-sided polygon) can be calculated using the formula that relates the height to the side length. For a regular dodecagon, the height is given by \( h = (2 + \sqrt{3}) \times S \), where S is the length of one side.
The calculator uses the height formula:
Where:
Explanation: The formula accounts for the geometric properties of a regular dodecagon, where the height is directly proportional to the side length with a constant factor of \( (2 + \sqrt{3}) \).
Details: Calculating the height of a dodecagon is important in various geometric and architectural applications, including design, construction, and spatial planning where regular dodecagonal shapes are used.
Tips: Enter the side length of the dodecagon in meters. The value must be valid (side length > 0).
Q1: What is a dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. A regular dodecagon has all sides equal and all interior angles equal.
Q2: Why is the formula \( h = (2 + \sqrt{3}) \times S \)?
A: This formula derives from the geometric properties of a regular dodecagon, specifically the relationships between its side length and the distances between parallel sides.
Q3: Can this formula be used for irregular dodecagons?
A: No, this formula applies only to regular dodecagons where all sides and angles are equal. Irregular dodecagons require different methods for height calculation.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering, and design where dodecagonal shapes appear in structures, patterns, and decorative elements.
Q5: How accurate is this formula?
A: The formula is mathematically exact for regular dodecagons. The accuracy of the result depends on the precision of the input side length measurement.