Names Of Shapes: Polygon Names, Quadrilaterals And 3D Shapes
The short version
- Flat shapes with straight sides are polygons, and they’re named by how many sides they have: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).
- Most polygon names are a Greek number plus “gon,” which means angle. So a pentagon is literally “five angles.”
- Triangles and quadrilaterals get extra names based on their sides and angles, like isosceles, rhombus or trapezoid.
- Circles and ovals have curved edges, so they aren’t polygons. 3D shapes like cubes, prisms and cones are solids with their own set of names.
The names of shapes come mostly from counting: a polygon with 3 sides is a triangle, 4 sides a quadrilateral, 5 a pentagon, 6 a hexagon, 7 a heptagon, 8 an octagon, 9 a nonagon, and 10 a decagon. Past that, mathematicians often just say “n-gon,” like 13-gon.
Most names of shapes in school math follow that one pattern. Below is a full polygon names table by number of sides, the special names for triangles and quadrilaterals, curved shapes, the common 3D solids, and a few memory tricks that make the Greek prefixes stick.
Polygon names by number of sides
A polygon is a closed, flat shape made only of straight line segments. Every polygon has the same number of sides, corners (vertices) and angles. So once you know the name of the polygon, you know all three counts.
| Sides | Name | Interior angles add to | Each angle if regular |
|---|---|---|---|
| 3 | Triangle | 180° | 60° |
| 4 | Quadrilateral | 360° | 90° |
| 5 | Pentagon | 540° | 108° |
| 6 | Hexagon | 720° | 120° |
| 7 | Heptagon (or septagon) | 900° | about 128.57° |
| 8 | Octagon | 1,080° | 135° |
| 9 | Nonagon (or enneagon) | 1,260° | 140° |
| 10 | Decagon | 1,440° | 144° |
| 11 | Hendecagon (or undecagon) | 1,620° | about 147.27° |
| 12 | Dodecagon | 1,800° | 150° |
| 20 | Icosagon | 3,240° | 162° |
The angle sum comes from one formula: (n – 2) × 180°, where n is the number of sides. For a hexagon, that’s (6 – 2) × 180° = 4 × 180° = 720°. It works because you can split any polygon into n – 2 triangles from one corner, and every triangle’s angles add to 180°.
A few bigger names show up in puzzles and trivia: a 100-sided polygon is a hectogon, and a 1,000-sided one is a chiliagon. In class, “100-gon” is completely fine.
Memory tricks for the prefixes
- Pent = 5: the Pentagon building in Virginia has five sides.
- Hex = 6: “hex” and “six” both end in x. Honeycomb cells are hexagons.
- Oct = 8: an octopus has eight arms. Stop signs are octagons.
- Non = 9: sounds a little like “nine.”
- Dec = 10: a decade is ten years.
- Dodec = 12: “do” (two) plus “dec” (ten). Two plus ten.
Names of triangles
Every triangle gets two kinds of names: one for its sides and one for its angles.
| Name | Sorted by | What it means |
|---|---|---|
| Equilateral | Sides | All 3 sides equal (all angles 60°) |
| Isosceles | Sides | At least 2 sides equal |
| Scalene | Sides | No sides equal |
| Acute | Angles | All angles less than 90° |
| Right | Angles | One angle exactly 90° |
| Obtuse | Angles | One angle greater than 90° |
So a triangle with sides 3, 4 and 5 is a right scalene triangle: no equal sides, and one 90° angle. Check with the Pythagorean theorem: 3² + 4² = 9 + 16 = 25 = 5².
Names of quadrilaterals
Four-sided shapes have the most names, and they overlap, which is where kids get confused.
- Parallelogram: two pairs of parallel sides.
- Rectangle: a parallelogram with four right angles.
- Rhombus: a parallelogram with four equal sides.
- Square: four equal sides and four right angles. That makes it a rectangle and a rhombus at the same time.
- Trapezoid: at least one pair of parallel sides. (Some textbooks say exactly one pair, so check which one your kid’s class uses.)
- Kite: two pairs of equal sides that sit next to each other, not across from each other.
The trick is to read the names like a family tree. Every square is a rectangle, but a rectangle is a square only if all four sides match. Every rectangle is a parallelogram. A rhombus is a “pushed over” square: same equal sides, different angles.
Regular, irregular, convex and concave
A polygon’s name only tells you how many sides it has. Two more words describe what it looks like.
Regular vs irregular. A regular polygon has all sides equal and all angles equal, like a stop sign. An irregular polygon doesn’t. An L-shaped room outline is still a hexagon (count the sides: six), just an irregular one.
Convex vs concave. A convex polygon has every corner pointing outward. A concave polygon has at least one corner that caves in, with an interior angle over 180°. A classic five-pointed star outline is a concave decagon: 10 sides, 10 vertices.
Curved shapes and 3D shapes
Not all names of shapes come from counting sides. Shapes with curves don’t get polygon names, because polygons need straight sides.
- Circle: every point is the same distance from the center.
- Oval: an egg-like stretched curve. A precise, symmetric oval is called an ellipse.
- Semicircle: half a circle, closed off by the diameter.
Solid shapes take up space and have faces, edges and vertices. Here are the ones kids meet first.
| 3D shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Rectangular prism | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Square pyramid | 5 | 8 | 5 |
| Triangular pyramid | 4 | 6 | 4 |
A cylinder has two flat circular faces and one curved surface. A cone has one flat circular face, a curved surface and a single point at the top. A sphere is one curved surface with no edges or vertices.
A quick check for the table: for these solids, faces + vertices – edges = 2. For a cube, 6 + 8 – 12 = 2. That’s called Euler’s formula.
Common mistakes with shape names
- Calling a rotated square a diamond. “Diamond” isn’t a math name. A tilted square is still a square. A diamond-looking shape with unequal angles is a rhombus.
- Thinking a shape must be regular to count. A hexagon with uneven sides is still a hexagon.
- Saying a square isn’t a rectangle. It is. It meets every rule for a rectangle.
- Mixing up heptagon and hexagon. Hex has the x (six). Hept is seven.
- Counting sides wrong on concave shapes. Put a finger on one corner and tap every vertex as you go around. The count of vertices equals the count of sides.
Practice problems
- What is the name of a polygon with 8 sides?
- How many sides does a nonagon have?
- A triangle has sides 5 cm, 5 cm and 8 cm. Name it by its sides.
- A quadrilateral has four equal sides but no right angles. What is it?
- What do the interior angles of a hexagon add up to?
- How big is each interior angle of a regular decagon?
- A polygon’s interior angles add up to 1,260°. How many sides does it have, and what’s its name?
Answers
- Octagon.
- 9.
- Isosceles (two equal sides).
- Rhombus.
- (6 – 2) × 180° = 720°.
- (10 – 2) × 180° = 1,440°, and 1,440° ÷ 10 = 144°.
- 1,260 ÷ 180 = 7, and 7 + 2 = 9 sides. It’s a nonagon.
If your kid mixes up the names of shapes
Memorizing the names of shapes is the easy part. The harder part, and the one that matters later, is noticing attributes: counting sides and vertices carefully, spotting right angles, and seeing when sides are parallel or equal. Those are 2nd to 4th grade skills, and our guide to math skills by grade level shows where each lands.
A kid who can name a hexagon but can’t find its angle sum is usually missing multiplication fluency or the idea of angles adding up, which is the same thinking behind supplementary angles. If shape vocabulary is one of several things slipping, our list of signs a child is behind in math can help you tell a small gap from a bigger pattern.
Frequently asked questions
What is a 9-sided shape called?
A nonagon. You may also see enneagon, from the Greek word for nine. Both mean the same shape.
What is an 11-sided shape called?
A hendecagon, sometimes spelled undecagon. Its angles add up to 1,620°.
Is a circle a polygon?
No. Polygons are made of straight sides, and a circle is one continuous curve.
What’s the difference between a square and a rhombus?
Both have four equal sides. A square also has four right angles. A rhombus can lean, so its angles don’t have to be 90°.
How do you find the name of a polygon?
Count its sides, then match the number to the table above. If there’s no common name (like 15 sides), call it a 15-gon.
Find the actual gap
If geometry vocabulary won’t stick, or your kid names shapes fine but can’t reason about their angles and sides, the snag is often an earlier skill. Math Anon’s short adaptive assessment finds which specific skills are missing and lays them out in a written report.
Your kid then gets about 20 minutes a day of practice targeted to those gaps, and you see a weekly progress report. The assessment is $49, and it’s credited in full to your first month. Start the assessment or read about pricing.
