12 Sided Dodecagon Calculator

Dodecagon Apothem Formula:

\[ \text{Apothem} = \frac{s}{2 \times \tan(15^\circ)} \]

Apothem:

Perimeter:

Area:

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1. What is a Dodecagon?

A dodecagon is a 12-sided polygon. A regular dodecagon has all sides equal in length and all angles equal in measure (150° each). This calculator computes properties of a regular dodecagon.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Apothem} = \frac{s}{2 \times \tan(15^\circ)} \] \[ \text{Perimeter} = 12 \times s \] \[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]

Where:

\( s \) — Length of one side
\( 15^\circ \) — Half of the central angle (360°/12 sides / 2)

3. Properties of a Regular Dodecagon

Details: A regular dodecagon has:

12 sides of equal length
Internal angles of 150° each
Central angles of 30° each
12 lines of symmetry
Rotational symmetry of order 12

4. Using the Calculator

Tips: Enter the side length in any consistent unit (cm, inches, etc.). The calculator will output apothem, perimeter, and area in corresponding units and squared units.

5. Frequently Asked Questions (FAQ)

Q1: What is an apothem?
A: The apothem is the line from the center to the midpoint of a side, equivalent to the radius of the inscribed circle.

Q2: How is the 15° angle derived?
A: The central angle is 360°/12 = 30°. Half of this (15°) is used in the apothem calculation.

Q3: Can this calculator be used for irregular dodecagons?
A: No, this calculator only works for regular dodecagons where all sides and angles are equal.

Q4: What's the relationship between side and radius?
A: The radius (circumradius) R = s / (2 × sin(15°)) ≈ s / 0.5176

Q5: How accurate are the calculations?
A: Calculations are precise to 4 decimal places for the apothem and 2 decimal places for perimeter and area.