What Is a Shape With 9 Sides? | Nonagon Name Made Clear

A nine-sided figure is called a nonagon, and many math books also use the name enneagon.

You’ve seen shapes with three sides and four sides since grade school. Nine sides feels less familiar, yet the name is simple once you know the pattern that geometry uses for polygons. This page gives you the exact term, how to tell a true nine-sider from a close look-alike, and the angle facts that help with homework, drawing, design, and puzzles.

What Is a Shape With 9 Sides? Name And Meaning

A shape with nine straight sides is a nonagon. In many texts you’ll also see enneagon. Both names point to the same idea: “nine angles.” In class, “nonagon” is the one most teachers expect, so it’s the safest word to use on tests.

One fast way to check you’re dealing with a nonagon is to count corners, not edges. Each side ends at a corner, so a nine-sided figure must have nine corners too. If the drawing has a “dent” (an inward corner), it can still be a nonagon as long as the sides stay straight and the total corner count stays nine.

How A nine-sided shape fits into polygon naming

In geometry, a closed shape made of straight line segments is a polygon. Polygons get their common names from Greek or Latin number roots. That’s why a three-sider is a triangle and a five-sider is a pentagon. A nonagon follows the same idea.

The word parts help you remember it. “Nona-” connects to nine (think “ninth”). “-gon” points to angles. Put them together and you get “nine angles.” “Enneagon” uses the Greek root “ennea” for nine.

Nonagon, enneagon, and which one to write

Both words are accepted in math writing. If you’re working from a school textbook, match the term it uses. If you’re writing from scratch, pick “nonagon” and stick with it through the whole assignment so your reader never has to guess.

Regular vs irregular nonagons

Not every nine-sided shape looks neat. A nonagon can be regular or irregular.

• Regular nonagon: all sides have the same length and all interior angles match.
• Irregular nonagon: at least one side length or angle differs.

There’s one more split that matters. A nonagon can be convex or concave. Convex means every interior angle is less than 180°. Concave means at least one interior angle is greater than 180°, so the outline caves inward.

Angle facts you can use right away

Most questions about a nonagon come down to angles. You don’t need memorized tables if you know two core rules for polygons.

Sum of interior angles

For any n-sided polygon, the sum of interior angles is (n − 2) × 180°. For n = 9, that becomes (9 − 2) × 180° = 7 × 180° = 1260°.

Each interior angle in a regular nonagon

In a regular nonagon, all interior angles match, so you divide the total by 9: 1260° ÷ 9 = 140°.

Exterior angles

Walk around the outside of any convex polygon, turning the same direction at every corner. The exterior angles always add to 360°. For a regular nonagon, each exterior angle is 360° ÷ 9 = 40°.

If you want these relationships in a clean reference format, Wolfram’s page on nonagon properties lists the standard names and formulas used in geometry writing.

How to spot a true nine-sided figure in a messy diagram

Drawings in worksheets are rarely perfect. Lines overlap, corners get rounded, and labels hide edges. Use this quick routine.

1. Find the corners first. Mark each corner with a dot, even if the corner points inward.
2. Trace the outline once. Use your finger or a pencil to follow the boundary without lifting.
3. Count the straight segments. Curves don’t count as sides in polygon naming.
4. Check for breaks. If the shape has a gap, it isn’t a polygon yet.

A common trap is a shape that looks like nine sides but includes a tiny curve or an extra bend along one edge. A single bent edge can create two sides, so count segments, not “stretches that feel like one side.”

Common nonagon formulas and what each one tells you

Once you know a figure is a nonagon, formulas help you answer most classroom tasks: angle measures, symmetry, and diagonals.

The diagonal count is a favorite. From any vertex of a nonagon, you can draw diagonals to all other vertices except itself and its two neighbors. That gives 9 − 3 = 6 diagonals from one vertex. Counting all vertices gives 9 × 6, then divide by 2 because each diagonal got counted twice. Total diagonals: (9 × 6) ÷ 2 = 27.

Regular nonagons also have symmetry. A regular nonagon has 9 lines of symmetry and rotational symmetry of order 9, meaning a turn of 40° lines it back up with itself.

If you want a clear picture of why the interior-angle rule works, Khan Academy’s lesson on sum of interior angles shows the triangle-splitting idea with visuals that match what many teachers draw on the board.

Reference table for a regular nonagon

The table below gathers the facts most people reach for when they’re solving problems, checking a drawing, or building a template.

Property	Regular Nonagon Value	How To Use It
Number of sides	9	Confirms the shape type
Number of vertices	9	Matches side count in any polygon
Sum of interior angles	1260°	Add all corner angles to check work
One interior angle	140°	Use when all angles match
Sum of exterior angles	360°	Works for any convex polygon
One exterior angle	40°	Handy for turning angles in drawings
Total diagonals	27	Counts all vertex-to-vertex diagonals
Lines of symmetry	9	Helps with folding and pattern checks
Rotational symmetry step	40°	Angle of rotation that repeats the shape

How to draw a regular nonagon by hand

You can sketch an irregular nonagon by plotting nine points and connecting them with straight edges. A regular nonagon is trickier because the sides and angles must match. The easiest classroom method uses a circle as a guide.

Method using a circle and 40° steps

1. Draw a circle and mark its center.
2. Draw one radius to a point on the circle. That point is your first vertex.
3. Use a protractor at the center to mark 40° steps around the circle.
4. Mark the nine points where the radii hit the circle.
5. Connect adjacent points with straight lines.

This works because the central angle between neighboring vertices is 360° ÷ 9, which is 40°. Equal central angles cut the circle into equal arcs, which gives equal chord lengths, which become equal side lengths.

Method using a compass and chord stepping

If you don’t have a protractor, you can still get close. Pick a circle size, then set your compass width to a chord length that repeats about nine times around the circle. Step that chord around the circle, mark each hit, then connect the marks. This method is less precise, so it’s better for art and craft projects than graded geometry.

How nonagons show up in real objects

Nine-sided shapes aren’t as common as hexagons or octagons, yet you can still spot them once your eye knows what to look for.

• Decorative tiles and borders: pattern makers mix different polygons, and a nine-sider can fill space in a repeating strip design.
• Signs and badges: a nonagon outline stands out because most people don’t see it every day.
• Board games and puzzles: designers use uncommon polygons to keep pieces from feeling like standard squares or hexes.

When you see a “rounded nonagon” in a logo, the edges may be slightly curved. In strict geometry that isn’t a nonagon anymore, since polygon sides must be straight. In everyday talk, people still call it a nonagon because the design reads as nine sides.

Second table: Quick checks for homework and design

Use these checks when you’re not sure whether a task is asking for a regular nonagon, an irregular one, or something else.

Task	Fast Check	What To Write Down
Name the shape	Count straight sides and corners	Nonagon (enneagon is accepted in many texts)
Find interior angle sum	Use (n − 2) × 180°	1260° for n = 9
Find one interior angle	Only if it’s regular	140°
Find one exterior angle	Only if it’s convex and regular	40°
Count diagonals	Use n(n − 3)/2	27 diagonals
Sketch a regular nonagon	Mark 40° at the center of a circle	Connect adjacent points with straight edges
Spot concave vs convex	Check for any inward corner	Concave if one interior angle is over 180°

Mistakes that cost points on worksheets

Most wrong answers around nine-sided figures come from small slips, not hard math. Here are the ones teachers see again and again.

Counting curved edges as sides

A polygon side is a straight segment. If the boundary is curved, the figure may still have nine “sections,” yet it won’t be a nonagon in strict geometry terms.

Using the regular angle value on an irregular shape

140° is only for a regular nonagon. If the diagram shows unequal sides or angles, you can still use 1260° as the total interior-angle sum, then solve for missing angles using that total.

Mixing up interior and exterior angles

Interior angles sit inside the shape. Exterior angles are the turns you make when you walk around the outside. On drawings, labels can make them look similar. If an angle is outside the boundary, treat it as exterior.

A compact checklist to finish a nonagon question

• Confirm the shape is closed and made of straight segments.
• Count vertices; a nine-sider has nine corners.
• Write the name: nonagon (enneagon is a common alternate term).
• Use 1260° for total interior angles, then split it only if the shape is regular.
• For regular cases, use 140° interior and 40° exterior.
• Use 27 for total diagonals when asked.