Tetradecagon — Definition, Formula & Examples

A tetradecagon is a polygon with 14 sides and 14 vertices. A regular tetradecagon has all sides equal in length and all interior angles equal in measure.

A tetradecagon is a closed, simple polygon composed of exactly 14 line segments (sides) meeting at 14 vertices. In its regular form, it exhibits 14-fold rotational symmetry, with each interior angle measuring $\frac{(14-2) \cdot 180°}{14} \approx 154.29°$ .

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of all interior angles of the polygon
$n$ = Number of sides (14 for a tetradecagon)

Worked Example

Problem: Find the sum of the interior angles of a tetradecagon and the measure of each interior angle if the tetradecagon is regular.

Step 1: Apply the interior angle sum formula with n = 14.

S = (14 - 2) \times 180° = 12 \times 180° = 2160°

Step 2: For a regular tetradecagon, divide the total by 14 to find each angle.

\text{Each angle} = \frac{2160°}{14} \approx 154.29°

Answer: The interior angles sum to 2160°. Each angle in a regular tetradecagon measures approximately 154.29°.

Why It Matters

Tetradecagons appear in tiling patterns and architectural designs. Studying polygons with many sides reinforces the general angle-sum formula and builds intuition for how polygons approximate circles as the number of sides increases.

Common Mistakes

Mistake: Confusing a tetradecagon (14 sides) with a tetrahedron (a 3D solid with 4 triangular faces).

Correction: "Tetradeca-" means 14 and refers to sides of a flat polygon, while "tetra-" means 4 and "-hedron" refers to faces of a solid. Count the prefix carefully.