Tridecagon — Definition, Formula & Examples

A tridecagon is a polygon with 13 sides and 13 angles. A regular tridecagon has all sides equal in length and all interior angles equal.

A tridecagon is a 13-gon, a closed plane figure bounded by 13 straight line segments (edges) meeting at 13 vertices. In its regular form, it exhibits 13-fold rotational symmetry with each interior angle measuring $\frac{(13-2) \cdot 180°}{13} \approx 152.31°$ .

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of interior angles
$n$ = Number of sides (13 for a tridecagon)

Worked Example

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

Step 1: Use the interior angle sum formula with n = 13.

S = (13 - 2) \times 180° = 11 \times 180° = 1980°

Step 2: For a regular tridecagon, divide the total by 13 to find each angle.

\text{Each angle} = \frac{1980°}{13} \approx 152.31°

Answer: The interior angles sum to 1980°. Each angle in a regular tridecagon measures approximately 152.31°.

Why It Matters

Studying polygons with many sides, like the tridecagon, reinforces the general interior angle sum formula and shows how it applies regardless of side count. This builds confidence with the pattern before moving to n-gon proofs in geometry courses.

Common Mistakes

Mistake: Confusing a tridecagon (13 sides) with a dodecagon (12 sides) or a tetradecagon (14 sides).

Correction: The prefix "tri-deca" means three-and-ten, so a tridecagon always has 13 sides. A dodecagon has 12 and a tetradecagon has 14.