Octadecagon — Definition, Formula & Examples

An octadecagon is a polygon with 18 sides and 18 angles. A regular octadecagon has all sides equal in length and all interior angles equal.

An octadecagon is an 18-gon, a closed plane figure composed of 18 straight line segments (sides) connected end-to-end. In its regular form, it exhibits 18-fold rotational symmetry, with each interior angle measuring 160°.

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of all interior angles
$n$ = Number of sides (18 for an octadecagon)

Worked Example

Problem: Find the measure of each interior angle of a regular octadecagon.

Step 1: Use the interior angle sum formula with n = 18.

S = (18 - 2) \times 180° = 16 \times 180° = 2880°

Step 2: Since a regular octadecagon has 18 equal angles, divide the sum by 18.

\text{Each angle} = \frac{2880°}{18} = 160°

Answer: Each interior angle of a regular octadecagon measures 160°.

Why It Matters

Octadecagons appear in tiling patterns and architectural designs where near-circular shapes are built from straight edges. Knowing how to work with many-sided polygons prepares you for geometry problems on standardized tests that use the general angle sum formula.

Common Mistakes

Mistake: Confusing the prefix 'octa-' (8) with 'octadeca-' (18) and thinking an octadecagon has 8 sides.

Correction: The prefix 'octadeca-' means 18 (from Greek for 8 + 10). An 8-sided polygon is an octagon.