What Is a Polygon With 8 Sides? | Octagon Facts Explained

An eight-sided polygon is called an octagon, and it has eight angles, eight vertices, and predictable angle rules in geometry.

If you’re studying shapes, doing homework, or brushing up on geometry terms, this one comes up a lot. The name for a polygon with 8 sides is octagon.

That’s the direct answer. But there’s more to know if you want to spot one quickly, solve class problems, or avoid mixing it up with other polygons.

An octagon can be regular (all sides and angles match) or irregular (they don’t). It can also be convex (no inward “dent”) or concave (one or more angles push inward). Those labels matter when you move from naming a shape to solving angle and perimeter questions.

This article walks through the name, parts, angle rules, diagonal count, common examples, and the formulas students use most often. If you’ve seen a stop sign and thought, “That shape has a special name,” you were right.

What Is a Polygon With 8 Sides In Geometry Terms?

A polygon with 8 sides is an octagon. In geometry, polygons are flat closed shapes made of straight line segments. So an octagon must be:

• 2D (flat)
• Closed (no gaps)
• Made with straight sides
• Built from exactly 8 sides

If a shape has curved edges, it isn’t a polygon. If it has eight sides but the lines don’t close, it still isn’t a polygon.

The word comes from roots that refer to “eight” and “angles.” That matches what you see in the shape: eight sides and eight angles. Dictionary definitions from established references describe an octagon as a flat shape or polygon with eight sides and eight angles, which matches school geometry use. Britannica’s octagon definition states this plainly.

Why Students Mix It Up With Other Shapes

It’s easy to confuse an octagon with a hexagon or decagon when you’re moving fast. The fix is simple: count the sides one by one and mark each corner with a finger or pencil as you go.

Many mistakes happen when a shape is stretched or tilted. Orientation does not change the name. A tall octagon, a wide octagon, and a slanted octagon are all still octagons if they keep 8 straight sides.

Octagon Vs Other Common Polygons

Here’s the quick pattern students use in class: 5 sides is pentagon, 6 is hexagon, 7 is heptagon, 8 is octagon, 9 is nonagon, 10 is decagon. Once you lock in that sequence, octagon questions feel much easier.

Parts Of An Octagon You Should Know

When teachers ask about an octagon, they may not stop at the name. They may ask for vertices, angles, diagonals, or side lengths. These are the parts you’ll see most often.

Sides, Vertices, And Angles

An octagon has:

• 8 sides
• 8 vertices (corner points)
• 8 interior angles
• 8 exterior angles (one at each vertex, if extended)

That one-to-one pattern helps when checking your work. If you counted 8 sides but only 7 vertices, you missed a corner.

Regular Vs Irregular Octagon

A regular octagon has all sides equal and all angles equal. This is the version used in many textbook formula questions.

An irregular octagon still has 8 sides, but side lengths or angle measures can differ. You can still call it an octagon, since the side count is what names the shape.

Convex Vs Concave Octagon

A convex octagon has no inward corners. All interior angles stay below 180°.

A concave octagon has at least one inward corner. One or more interior angles are greater than 180°.

Students often meet convex octagons first. Concave ones show up later in classification and angle practice.

Angle Rules For An Octagon

This is where many geometry questions land. You may be asked for the sum of the interior angles, each angle in a regular octagon, or the exterior angle.

Sum Of Interior Angles

The interior angle sum for any polygon with n sides is:

(n − 2) × 180°

For an octagon, n = 8:

(8 − 2) × 180° = 6 × 180° = 1080°

So the total of all interior angles in any octagon is 1080°. This formula is a standard polygon rule taught in school geometry; Khan Academy teaches the same interior-angle-sum pattern for polygons. Khan Academy’s polygon angle lesson shows the formula and how it works.

Each Interior Angle In A Regular Octagon

If the octagon is regular, all 8 interior angles are equal. Divide the total by 8:

1080° ÷ 8 = 135°

So each interior angle in a regular octagon is 135°.

Each Exterior Angle In A Regular Octagon

For any regular polygon, the exterior angles add to 360°. A regular octagon has 8 equal exterior angles, so:

360° ÷ 8 = 45°

That gives 45° for each exterior angle of a regular octagon.

Octagon Fact	Value / Rule	What It Means In Class
Name	Octagon	A polygon with 8 sides
Number Of Sides	8	Count sides to identify the shape
Number Of Vertices	8	Each corner is a vertex
Number Of Interior Angles	8	One interior angle at each vertex
Interior Angle Sum	1080°	Use (n − 2) × 180° with n = 8
Regular Octagon Interior Angle	135°	1080° divided by 8 equal angles
Regular Octagon Exterior Angle	45°	360° divided by 8 equal angles
Diagonal Count	20	Connect non-adjacent vertices
Perimeter (Regular)	8 × side length	Add all sides; same shortcut in regular case

How To Tell If A Shape Is An Octagon

When a worksheet gives strange drawings, students can second-guess themselves. A clean check routine helps.

A Fast Identification Method

1. Check that the shape is flat and closed.
2. Make sure all edges are straight line segments.
3. Count the sides carefully.
4. If the count is 8, it’s an octagon.

That method works for regular and irregular versions. You do not need equal sides to call it an octagon.

Shapes That Are Not Octagons

A shape with curves is not a polygon. A shape with 8 sides and one curved edge is not an octagon. A shape with 8 straight segments that crosses over itself may be treated differently depending on the class level and the exact lesson.

For most school questions, the expected octagon is a standard simple polygon with eight straight sides that does not cross itself.

Regular Octagon Formulas Students Use Most

Many school tasks ask for perimeter and area. Perimeter comes up early. Area appears later, often in algebra or geometry units.

Perimeter Of A Regular Octagon

If each side has length s, then:

Perimeter = 8s

Say each side is 6 cm. Then the perimeter is 8 × 6 = 48 cm.

If the octagon is irregular, add all eight side lengths one by one.

Area Of A Regular Octagon

One common formula is:

Area = 2(1 + √2)s²

This formula is for a regular octagon. If the octagon is irregular, area is not found with one simple side-length shortcut. You may need to split the shape into smaller pieces.

Diagonal Count Of An Octagon

The number of diagonals in an n-sided polygon is:

n(n − 3) ÷ 2

For an octagon:

8(8 − 3) ÷ 2 = 8 × 5 ÷ 2 = 20

So an octagon has 20 diagonals.

Question Type	Formula For A Regular Octagon	Output
Perimeter	8s	Total boundary length
Area	2(1 + √2)s²	Square units
Interior Angle (Each)	(n − 2) × 180° ÷ n with n = 8	135°
Exterior Angle (Each)	360° ÷ 8	45°
Diagonals	n(n − 3) ÷ 2 with n = 8	20

Real-Life Octagon Examples You Already Know

The most common example is a stop sign. In many countries, stop signs use an octagonal shape, which makes them easy to recognize at a glance.

You may also spot octagons in floor tiles, table designs, windows, wall mirrors, and school art projects. Once you know the side count, the shape starts showing up all over the place.

Why The Shape Gets Used

An octagon feels balanced and easy to spot. It gives more edges than a square or hexagon while still staying simple enough for signs and designs.

In geometry class, it also works well for teaching polygon rules because it sits in a nice middle range: not too small, not too large, and rich enough for angle and diagonal practice.

Common Octagon Mistakes And Easy Fixes

Mixing Up Sides And Angles

Students may count 8 corners and assume 8 sides without checking. In a standard closed polygon, those counts match, but you still need to verify the shape uses straight segments.

Assuming Every Octagon Is Regular

This is a common slip. “Octagon” tells you the number of sides, not that all sides match. If a question says regular octagon, then use equal-angle and equal-side shortcuts.

Using The Wrong Angle Formula

Another common slip is mixing up interior-angle sum and one interior angle in a regular polygon. For an octagon:

• Interior angle sum = 1080°
• Each interior angle (regular octagon) = 135°

If you write 1080° as one angle, your answer will look off right away. A single angle that large would not fit a regular octagon.

A Simple Way To Remember It

Use this memory line: Octagon = 8 sides. Then attach the regular-octagon angle facts:

• Each inside angle = 135°
• Each outside angle = 45°
• All inside angles together = 1080°

If you’re revising for a test, write those four facts on a small note and solve two or three practice problems. That repetition builds speed.

Final Answer

A polygon with 8 sides is called an octagon. If all sides and angles are equal, it is a regular octagon; if not, it is an irregular octagon. In a regular octagon, each interior angle is 135°, each exterior angle is 45°, and the interior angles add up to 1080°.