Hexadecagon — Definition, Formula & Examples

A hexadecagon is a polygon with 16 sides and 16 angles. A regular hexadecagon has all sides equal in length and all interior angles equal in measure.

A hexadecagon is a 16-gon, a closed plane figure bounded by 16 straight line segments. In its regular form, each interior angle measures 157.5° and each exterior angle measures 22.5°.

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of interior angles
$n$ = Number of sides (16 for a hexadecagon)

Worked Example

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

Step 1: Apply the interior angle sum formula with n = 16.

S = (16 - 2) \times 180° = 14 \times 180° = 2520°

Step 2: For a regular hexadecagon, divide the total by 16 to find each angle.

\text{Each angle} = \frac{2520°}{16} = 157.5°

Answer: The sum of interior angles is 2520°, and each interior angle of a regular hexadecagon measures 157.5°.

Why It Matters

Hexadecagons appear in architecture and coin design — the James Webb Space Telescope's mirror segments approximate a hexadecagonal shape. Knowing how to work with many-sided polygons prepares you for geometry problems that go beyond basic shapes.

Common Mistakes

Mistake: Confusing a hexadecagon (16 sides) with a hexagon (6 sides) because both names start with 'hex'.

Correction: The prefix 'hexa' means 6, but 'hexadeca' means 16 (from the Greek for 'six and ten'). Count the prefix carefully.