Think through a tangram
A tangram lets you reason with shape, orientation and area. Instead of moving pieces at random, identify a feature of the target and test which piece or combination can produce it.
By Zehano · Original AI-assisted explanation and worked example · Updated 16 October 2026 · Editorial approach
A worked example
Begin with the two smallest congruent right triangles. Place them along their longest sides to form a square, then rearrange them to make a larger right triangle. The total area stays the same even though the outline changes. That observation gives you a practical way to inspect a target: a small square-shaped region might be filled by the square piece or by two smaller triangles, depending on what the rest of the outline requires. Try one arrangement, then look at the remaining gap. If its edges cannot be matched by the remaining pieces, revisit the assumption instead of forcing an overlap. A small physical sketch can also help you separate the target’s outline from distracting internal boundaries.
Try it in three steps
- Inventory the seven pieces before starting. Notice which have matching sizes, which have right angles, and which pairs can combine into a useful larger shape.
- Work from a distinctive boundary such as a sharp tip, a long straight edge or an inward corner. Rotate a candidate piece and inspect the space it leaves before committing the next piece.
- Check coverage and overlap separately. Pieces can appear to trace the outside silhouette while still overlapping internally or leaving a small gap. Inspect the interior as well as the outline.
What to watch for
Turning and reflecting a shape are different operations. In a standard tangram, the parallelogram can require a flip for some arrangements. Follow the controls and target rules of the particular activity; do not assume a rotation alone can produce every reflected position.
Apply it to your own material
Choose one topic from your current course or project. Write down the question you want to answer, make an attempt, and keep a note of how you checked it. Use the example above as a pattern; replace its subject matter and assumptions rather than copying an answer into a different task.
Open Tangram Studio ↗