Free printable open and closed shapes

Grades K–2A closed shape has no gaps — you could color it in. An open one has loose ends. Print it for the wall, or sort the figures below and see why closed is half of what makes a polygon.

Open and Closed Shapes math chart for kids Tap the chart to open it at full size

Open or closed?

Decide whether each figure is open or closed. The reason appears as soon as you choose.

Closed does not mean straight. A circle is closed, and so is a wobbly blob — the test is only whether the line meets itself with no gap.

The zigzag is the useful one. It is made of perfectly straight lines and is still open, because the ends never join. Straight sides and closed are two separate requirements, and a polygon needs both.

Open, or closed?

  • Triangle
  • Broken triangle
  • Circle
  • Arc
  • Zigzag
  • Pentagon
How you are doing
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Closed means the line joins back to where it started, with no gaps.

How to use this open and closed shapes chart at home

Use the coloring test. Could you color it in without the color escaping? Children answer that instantly and correctly, long before they can explain what closed means.

Draw shapes with a deliberate gap and ask. A triangle with one side missing is the clearest example there is, and drawing it yourself makes the gap obvious.

Then use string or a shoelace. Lay it out with the ends apart, then join them. The same piece of string goes from open to closed with one movement.

Closed is half of being a polygon

A polygon needs two things: every side straight, and the whole outline closed. Most charts emphasize the straight part and skip the closed part, because closed feels obvious.

It is not obvious to a five-year-old. A zigzag is made entirely of straight lines and is not a polygon, and seeing that stated explicitly saves confusion later.

Putting the two rules side by side also explains the circle. Closed but curved, so not a polygon. The zigzag is straight but open, so also not. You need both.

Why closed shapes have an inside

The moment an outline joins up, it divides the paper into two parts: inside and outside. That division is what makes area possible.

An open figure has no inside, which is why you cannot shade it in or measure its area. It has a length, but not a perimeter — perimeter means the distance around something.

This is worth saying because it makes closed feel like a useful property rather than an arbitrary label.

Where open and closed usually go wrong

Thinking closed means straight. A circle is closed and curved.

Missing a small gap. A shape drawn almost closed is still open, and looking at the corners carefully is the check.

Calling a zigzag a shape. Straight lines are not enough on their own.

Assuming open figures have an area. There is no inside to measure.

After the chart goes up

A chart explains the idea but gives a child nothing to do. These do the rest.

Everything at this level: Kindergarten math · Grade 1 math · Grade 2 math

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Questions parents ask

What is a closed shape?

A figure whose outline joins back to where it started, leaving no gaps. Because the inside is completely enclosed, you could color it in without the color escaping.

What is an open shape?

A figure with loose ends that do not meet. There is no inside, because there is nothing to be inside of. An arc and a zigzag are both open.

Is a circle a closed shape?

Yes. Closed is about gaps, not straightness. A circle meets itself perfectly, so it is closed — it just is not a polygon, because its edge is curved.

Why does closed matter?

Because area, perimeter and the whole idea of a polygon depend on it. A shape with a gap has no inside to measure and no outline to go around.

How can a child test whether a shape is closed?

Ask whether you could color it in without the color leaking out. It is a genuinely reliable test and children find it obvious in a way that talk of endpoints is not.

What grade is this open and closed shapes chart for?

Kindergarten through Grade 2. It usually arrives alongside the first shape names, because closed is part of what makes something a shape at all.

Is this open and closed shapes 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.