Not every shape with straight sides gets the same name. Learn how to tell polygons apart by counting sides, checking whether they're regular or irregular, and spotting the difference between convex and concave — then test yourself with real shapes.
A polygon is a closed, flat shape made only of straight line segments. To count as a polygon, a shape has to follow three rules:
1. It must be closed — every side connects to form a complete loop, with no gaps.
2. Every side must be straight — no curves allowed.
3. Sides only meet at their endpoints (the vertices, or corners) — they never cross each other.
Before you classify any shape, ask yourself: is it closed, is every side straight, and do the sides avoid crossing? If you can answer "yes" to all three, you're looking at a polygon.
Once you know a shape is a polygon, its name comes from how many sides (and vertices) it has. Most polygon names come from Greek number roots — "tri" means three, "penta" means five, and so on.
The word "polygon" itself comes from Greek: poly means "many" and gon means "angle." So a polygon is literally a shape with "many angles" — and the number of angles always matches the number of sides.
Two polygons can have the same number of sides and still look completely different. That's where regular and irregular come in.
A regular polygon has all sides the same length and all angles the same measure. An irregular polygon has sides and/or angles that aren't all equal.
All 6 sides and all 6 angles are equal.
Still 6 sides — but they're different lengths.
Both shapes above are hexagons because they each have 6 sides. The number of sides tells you the name; whether the sides and angles match tells you if it's regular or irregular.
Polygons can also be classified by their overall shape. A convex polygon has no indentations — every interior angle is less than 180°, and the shape always bulges outward. A concave polygon has at least one interior angle greater than 180°, which pulls part of the shape inward.
Every corner points outward. No dents.
One corner points inward, like a bite taken out.
"Concave" contains the word cave — picture a cave carved into the side of the shape. If any part looks like it's caving in, the polygon is concave. Otherwise, it's convex.
Look at the shape below and classify it three ways: its name (based on sides), whether it's regular or irregular, and whether it's convex or concave.
Pick one answer in each row, then check your work.
Every shape below is a quadrilateral because it has 4 sides — but some quadrilaterals have extra-special properties that earn them a more specific name. In the chart below, every shape inside a box is also everything that box is nested inside.
The shapes where the two circles overlap are Squares — they have 4 right angles and 4 equal sides, so they belong to both the Rectangle group and the Rhombus group at the same time.
Most elementary math books say a trapezoid has exactly one pair of parallel sides. (Some higher-level textbooks use an "at least one" definition instead — your teacher will let you know which one your class uses.)
Look at the shape and select every label that applies. Remember: a square is also a rectangle, a parallelogram, and a quadrilateral — all at the same time!
Select all the labels that correctly describe the shape, then check your work.