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Tangram Hat

The tangram “Hat” is one of the hardest tangram figures on this site: expect to get stuck at least once before it clicks. Like every figure here, it uses all seven pieces — two large triangles, one medium triangle, two small triangles, a square and a parallelogram — with nothing left over and nothing missing. Below you will find the dark silhouette to solve, the complete solution and a clean outline to print and color.

Tangram Hat puzzle silhouette
Puzzles + solutions (PDF)Color pieces (PDF)

Hat

Tangram Hat puzzle silhouette
Show solutionTangram Hat solution

How to build it, step by step

  1. Place the two large triangles first. Together they are always half of the figure, and their long edges usually form the longest side of the silhouette.
  2. Add the medium triangle and the square next to them; they fill the wide middle areas.
  3. Finish with the two small triangles and the parallelogram — they make the fine details: corners, tips and narrow ends.

Good news in this figure: the parallelogram keeps its normal orientation, so you never need to flip it. If a space seems impossible, the problem is almost always a large triangle placed too early in the wrong corner.

Print and color the Hat

Tangram Hat coloring outlinePrint this outline and color each piece before or after solving it — coloring first is a good memory trick for young children. The same figure is in the figures PDF on the printable tangram page, together with the piece templates.

Play the Hat online

You can also solve this exact figure in the online tangram game: drag the seven pieces onto the dark silhouette and the game tells you when the hat is complete. All the other figures live on the tangram shapes page.

FAQ

Is the tangram hat easy or hard?
It is one of the hardest tangram figures on this site: expect to get stuck at least once before it clicks.
Do I need to flip the parallelogram for the hat?
No. In this figure the parallelogram keeps its normal orientation.
Can I print the tangram hat?
Yes: print the outline on this page, or download the figures PDF from the printable tangram page — it includes this figure, its solution and the seven pieces.

More tangram pages

Free for personal and classroom use.