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The inradius of a dodecagon (12-sided polygon) is the radius of the circle that fits perfectly inside the dodecagon, touching all its sides. It represents the distance from the center to any side of the dodecagon.
The calculator uses the formula:
Where:
Explanation: This formula calculates the inradius based on the area of the dodecagon, incorporating the mathematical constant √3 which is inherent to the geometry of regular 12-sided polygons.
Details: Calculating the inradius is important in geometry and various engineering applications where the relationship between a polygon's area and its inscribed circle needs to be determined. It helps in understanding the spatial properties and proportions of dodecagonal shapes.
Tips: Enter the area of the dodecagon in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding inradius.
Q1: What is a dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. When all sides and angles are equal, it's called a regular dodecagon.
Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching the sides), while the circumradius is the radius of the circumscribed circle (passing through the vertices).
Q3: Can this formula be used for irregular dodecagons?
A: No, this formula specifically applies to regular dodecagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is used in architecture, mechanical design, and various engineering fields where dodecagonal shapes are employed, such as in certain types of bolts, nuts, or architectural elements.
Q5: How accurate is the calculation?
A: The calculation is mathematically precise for regular dodecagons, with accuracy depending on the precision of the input area value.