Hectogon (100-sided Polygon) — Definition, Formula & Examples

A hectogon is a polygon with 100 sides and 100 vertices. Because it has so many sides, a regular hectogon looks nearly identical to a circle.

A hectogon is a 100-gon — a closed, plane figure composed of 100 straight line segments (sides) meeting at 100 vertices. A regular hectogon has all sides of equal length and all interior angles of equal measure.

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of interior angles of the polygon
$n$ = Number of sides (100 for a hectogon)

Worked Example

Problem: Find the measure of one interior angle of a regular hectogon.

Step 1: Use the interior angle sum formula with n = 100.

S = (100 - 2) \times 180° = 98 \times 180° = 17{,}640°

Step 2: Since a regular hectogon has 100 equal angles, divide the sum by 100.

\text{Each angle} = \frac{17{,}640°}{100} = 176.4°

Answer: Each interior angle of a regular hectogon measures 176.4°.

Why It Matters

The hectogon illustrates how polygons with many sides approximate circles. Archimedes used 96-sided polygons to estimate π, and a hectogon serves the same idea — connecting polygon geometry to the study of curves.

Common Mistakes

Mistake: Confusing a hectogon (100 sides) with a hexagon (6 sides) because the names sound similar.

Correction: The prefix "hecto-" means 100 (as in hectometer), while "hexa-" means 6. Count the prefix carefully.