Regular Dodecagon — Definition, Formula & Examples

A regular dodecagon is a 12-sided polygon where every side has the same length and every interior angle has the same measure. Each interior angle equals 150°.

A regular dodecagon is an equilateral and equiangular polygon with 12 vertices, 12 sides of equal length, and 12 congruent interior angles, each measuring $\frac{(12-2) \cdot 180°}{12} = 150°$ .

Key Formula

A = 3(2 + \sqrt{3})\,s^2

Where:

$A$ = Area of the regular dodecagon
$s$ = Length of one side

Worked Example

Problem: Find the area of a regular dodecagon with side length 4 cm.

Write the formula: Use the area formula for a regular dodecagon.

A = 3(2 + \sqrt{3})\,s^2

Substitute the side length: Replace

s

with 4 cm.

A = 3(2 + \sqrt{3})(4)^2 = 3(2 + \sqrt{3})(16)

Compute the result: Evaluate using

\sqrt{3} \approx 1.732

A = 48(2 + 1.732) = 48(3.732) \approx 179.1 \text{ cm}^2

Answer: The area is approximately 179.1 cm².

Why It Matters

Regular dodecagons appear in architecture, tiling patterns, and coin designs (some coins approximate this shape). Understanding them reinforces the general formulas for regular polygons, which are tested throughout high school geometry.

Common Mistakes

Mistake: Confusing a dodecagon (12 sides) with a decagon (10 sides).

Correction: The prefix "dodeca-" means 12 in Greek, while "deca-" means 10. Count the sides or recall the prefix to distinguish them.