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What Is a Shape with Ten Sides Called?
If you have ever wondered what is a shape with ten sides called, the answer is a decagon.
The name of the shape with ten sides comes straight from ancient Greek. Deka means “ten” and gonia means “angle” or “corner.” Put them together and you get “ten angles.” Since every corner of a closed polygon comes with a side, a decagon always has ten sides, ten vertices (corners) and ten interior angles.
That Greek naming habit runs through all of geometry. Penta gives us the pentagon (five), hexa the hexagon (six) and octo the octagon (eight). The decagon simply continues the family tradition.
Geometry Quick Guide
The Quick Facts: A Decagon at a Glance
Before we go deeper, here's a snapshot of a shape with ten sides.
| Property | Value |
|---|---|
| Number of sides | 10 |
| Number of vertices | 10 |
| Sum of interior angles | 1,440° |
| Each interior angle (regular decagon) | 144° |
| Each exterior angle (regular decagon) | 36° |
| Number of diagonals | 35 |
💡 Remember: The word “regular” matters! A regular decagon has ten equal sides and ten equal interior angles, while an irregular decagon does not.
Regular vs. Irregular Decagons
Not every decagon looks the same. Geometry sorts them into two main camps.
Regular decagon: All ten sides are equal in length and all ten angles are equal. This is the tidy, symmetrical version most people picture. It has ten lines of symmetry and looks beautifully balanced.
Irregular decagon: The sides and angles can be any mix of sizes, as long as there are ten straight sides forming a closed shape. Think of a stretched, squashed or lopsided version. It is still a decagon, just a free-spirited one.
There is also a third idea worth knowing: decagons can be convex (all corners point outward) or concave (at least one corner dents inward, like a cave).
Geometry Made Simple
The Math Behind the Shape
You don't need to be a math whiz to enjoy this part. A few simple formulas unlock almost everything about a decagon.
1. Sum of Interior Angles
Any polygon with n sides has interior angles that add up to (n − 2) × 180°. For ten sides:
In a regular decagon, divide that by ten and each angle is 144°. That's wider than the 135° angle of an octagon, which helps explain the decagon's broad shape.
2. Counting Diagonals
A diagonal connects two corners that are not neighbors. The formula is n(n − 3) ÷ 2, so:
Draw them all inside a regular decagon and you'll get a fascinating web of crossing lines.
3. Area of a Regular Decagon
If each side has length a, the area is:
For example, a regular decagon with sides of 2 cm has an area of approximately 30.8 cm².
Math takeaway: A decagon has 10 sides, 1,440° in total interior angles, 35 diagonals, and an area that depends on its side length.
A Secret Link to the Golden Ratio
Here is the part that makes mathematicians smile. The regular shape with ten sides is deeply connected to the golden ratio, that famous number of roughly 1.618 that shows up in art, nature and architecture.
In a regular decagon, the distance from the center to any corner (the circumradius) equals the side length multiplied by the golden ratio. This tight relationship is also why the decagon sits so comfortably alongside the pentagon. Connect every other corner of a decagon and you get two interlocking pentagons. Ancient Greek geometers knew this, and it is one reason the regular decagon can be constructed using nothing more than a compass and a straightedge.
Where Do We See a Shape with Ten Sides in Real Life?
Perfect decagons are rarer in daily life than hexagons or octagons, but they appear in some surprising places.
Coins, Medals & Badges
Designers sometimes use ten-sided outlines to make an object distinctive and easy to recognize by touch.
Architecture & Design
Decagonal floor plans, gazebos, tiles, and windows can create a grand, almost circular feel while retaining straight edges.
Tabletop Games
The ten-sided die, or d10, is popular in role-playing games. It has ten faces, each bearing a number, and is not a true decagon.
Science & Crystals
Researchers study decagonal quasicrystals, materials with unusual atomic arrangements and tenfold symmetry.
Art & Patterns
Islamic geometric art often features intricate repeating patterns. Tenfold symmetry also inspires striking geometric designs.
The Decagon's Starry Side: The Decagram
Connect the ten corners of a decagon by skipping some vertices instead of joining neighboring ones. This creates a decagram, a ten-pointed star.
How to Draw a Decagon
Create your own ten-sided polygon with these four simple steps.
Challenge yourself! Try constructing a decagon using a compass and straightedge, then explore how the golden ratio relates to regular polygons.
Frequently Asked Questions
Everything you need to know about a shape with ten sides.
What is a shape with ten sides?
It is called a decagon, a closed polygon made of ten straight sides and ten corners.
What is the name of the shape with ten sides?
The name is decagon, derived from Greek roots meaning “ten” and “angle.”
How many degrees are in a decagon?
The interior angles add up to 1,440°. In a regular decagon, each interior angle measures 144°.
Is a decagon the same as a decahedron?
No. A decagon is a flat, two-dimensional shape with ten sides. A decahedron is a three-dimensional solid with ten faces.
Remember: Decagon = 10 sides. The prefix “deca-” means ten!
