Free printable polygon chart
Grades 3–7Every polygon name from three sides up to twelve, arranged as a ladder — and the angle total climbing by exactly 180 degrees at every step. Print it for the wall, or climb the ladder below one rung at a time.
Tap the chart to open it at full size
Climb the ladder
Move up a rung at a time and watch two things change together: the name, and the total of the interior angles.
That total is the reason this is a ladder rather than a list. Every extra side adds exactly 180 degrees — a triangle is 180, a quadrilateral 360, a pentagon 540, and so on forever.
The reason is worth showing. Each new side lets you cut off one more triangle from inside the shape, and every triangle carries 180 degrees with it. That is why the formula is (n − 2) × 180: the number of triangles you can make is always two fewer than the number of sides.
- Its name
- Hexagon
- Sides and corners
- 6 sides · 6 corners
- Angles add up to
- 720°
Count the green numbers. Sides and corners always match, however many there are.
How to use this polygon ladder chart at home
Climb it in order rather than jumping about. The ladder only shows its pattern if you go up one rung at a time and watch the total change.
Predict before revealing. Once a child has seen 180, 360 and 540, ask what a hexagon will be before showing them. Getting 720 by adding rather than by formula is the better route.
Then draw the triangles. Pick a corner of a pentagon and draw lines to the other corners — three triangles appear. Doing that for a hexagon gives four. The formula stops being arbitrary.
Why every rung adds 180
Adding a side to a polygon adds exactly one more triangle to the inside, and a triangle always carries 180 degrees.
That is the whole explanation, and it means the angle total is never something to memorize. A child who forgets the formula can rebuild it by drawing triangles.
It also explains the minus two. Fixing one corner and drawing to all the others always produces two fewer triangles than there are sides, because the two neighboring corners are already joined to it.
The names, and when to stop using them
Penta, hexa, hepta, octa, deca — Greek number words, and once spotted they carry most of the list.
Past about eight sides, the names stop being useful. Hendecagon and dodecagon are correct and almost nobody says them; 11-gon and 12-gon are clearer and equally acceptable.
Telling children that mathematicians also give up on the names is worth doing. It removes the sense that there is an endless list to memorize.
Where the ladder usually goes wrong
Using the angle total when the question wanted one angle. Divide by the number of sides, and only if the polygon is regular.
Forgetting the minus two. It comes from the triangles, not from nowhere.
Assuming every polygon on a rung is regular. The angle total holds for any polygon with that many sides, lopsided or not.
Miscounting sides on an awkward shape, which then makes every later step wrong.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- geometry at Mathify Kids — every topic in this area, sorted by grade.
- naming 2D shapes worksheets — printable practice.
- types of angles worksheets — the next step once this is solid.
- perimeter worksheets — more practice in the same area.
Everything at this level: Grade 3 math · Grade 4 math · Grade 5 math · Grade 6 math · Grade 7 math
Charts that pair with this one
Charts that work well printed alongside this one.
-
Shapes by Number of Sides chart
-
Angles chart
-
Types of Quadrilaterals chart
-
Regular Shapes chart
-
Geometry chart
Last reviewed
Questions parents ask
What are the polygon names from 3 to 12 sides?
Triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, hendecagon and dodecagon. Beyond about seven sides, mathematicians often write 9-gon or 12-gon instead.
What is the sum of the interior angles of a polygon?
(n − 2) × 180 degrees, where n is the number of sides. A triangle gives 180, a quadrilateral 360, a pentagon 540. Each extra side adds another 180.
Why is the formula (n − 2) × 180?
Because you can cut any polygon into triangles by drawing lines from one corner, and you always get two fewer triangles than sides. Each triangle contributes 180 degrees, so the total is (n − 2) × 180.
How big is each angle in a regular polygon?
Divide the total by the number of sides. A regular hexagon has 720 divided by 6, which is 120 degrees per angle. This only works when the polygon is regular.
What is a polygon with 11 sides called?
A hendecagon, though undecagon is also used. Eleven and other awkward counts are exactly where the n-gon shorthand becomes more practical than the name.
What grade is this polygon ladder chart for?
Grades 3 to 7. The names arrive around Grade 3 or 4, and the angle sum formula around Grade 6 or 7.
Is this polygon ladder chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.