Is it called a hendecagon or an undecagon?

Both names refer to the same 11-sided polygon. "Hendecagon" comes from Greek (hendeka = eleven), while "undecagon" uses a Latin-Greek hybrid (undecim = eleven). Most modern geometry textbooks accept either name, though "hendecagon" is considered more etymologically consistent.

Hendecagon — Definition, Formula & Examples

A hendecagon is a polygon with 11 sides and 11 angles. It is also sometimes called an undecagon.

A hendecagon is an 11-gon — a closed, simple polygon composed of exactly 11 straight line segments (sides) meeting at 11 vertices. In a regular hendecagon, all sides are congruent and all interior angles are equal, each measuring $\frac{(11-2) \times 180°}{11} \approx 147.27°$ .

Key Formula

S = (n - 2) \times 180° = (11 - 2) \times 180° = 1620°

Where:

$S$ = Sum of interior angles of the hendecagon
$n$ = Number of sides (11 for a hendecagon)

How It Works

You can find the sum of interior angles of any hendecagon using the polygon angle-sum formula

(n-2) \times 180°

, where

n = 11

. This gives

1620°

for every hendecagon, whether regular or irregular. For a regular hendecagon, divide that total equally among the 11 angles to get each one. The number of diagonals, the apothem, and the area can also be computed from standard polygon formulas once you know the side length.

Worked Example

Problem: Find each interior angle and the number of diagonals in a regular hendecagon.

Step 1: Find the sum of interior angles using the formula.

S = (11 - 2) \times 180° = 9 \times 180° = 1620°

Step 2: Divide by 11 to get each interior angle of the regular hendecagon.

\text{Each angle} = \frac{1620°}{11} \approx 147.27°

Step 3: Use the diagonal formula for an n-sided polygon.

d = \frac{n(n-3)}{2} = \frac{11(11-3)}{2} = \frac{11 \times 8}{2} = 44

Answer: Each interior angle of a regular hendecagon is approximately 147.27°, and it has 44 diagonals.

Another Example

Problem: A regular hendecagon has a side length of 6 cm. Find its perimeter.

Step 1: A regular hendecagon has 11 equal sides.

Step 2: Multiply the side length by 11.

P = 11 \times 6 = 66 \text{ cm}

Answer: The perimeter is 66 cm.

Why It Matters

Hendecagons appear in geometry courses whenever you study polygon angle sums and generalize formulas beyond common shapes like pentagons or hexagons. Practicing with 11-sided figures builds fluency with the

(n-2) \times 180°

formula and prepares you for problems involving any

n

-gon on standardized tests. Some coin designs around the world, such as the Canadian dollar coin (loonie), use hendecagonal shapes for their distinctive feel.

Common Mistakes

Mistake: Using

n \times 180°

instead of

(n-2) \times 180°

for the angle sum.

Correction: Always subtract 2 from the number of sides before multiplying by 180°. For a hendecagon:

(11-2) \times 180° = 1620°

, not

11 \times 180° = 1980°

Mistake: Confusing a hendecagon (11 sides) with a decagon (10 sides) or dodecagon (12 sides).

Correction: Remember that "hendeca-" means eleven in Greek. A decagon has 10 sides and a dodecagon has 12.

Related Terms

Decagon — Polygon with one fewer side (10 sides)
Dodecagon — Polygon with one more side (12 sides)
Heptagon — Another named polygon (7 sides)
Apothem — Used to find a regular hendecagon's area
Diagonal of a Polygon — A hendecagon has 44 diagonals
Convex — A regular hendecagon is always convex
Concave — An irregular hendecagon can be concave