Tangram — Definition, Formula & Examples
A tangram is a puzzle made of seven flat geometric pieces, called tans, that fit together to form a square. You can rearrange the seven pieces to create hundreds of different shapes, such as animals, people, and letters.
A tangram is a dissection puzzle consisting of seven polygonal pieces — five right triangles (two large, one medium, two small), one square, and one parallelogram — obtained by partitioning a square along specific line segments. Any valid tangram figure uses all seven pieces without overlap.
How It Works
Start with a square divided into the seven tans. To solve a tangram puzzle, you look at a silhouette or outline and try to fill it exactly using all seven pieces, with no gaps and no overlapping. You can slide, rotate, and flip the pieces. The total area of the figure always equals the area of the original square, no matter what shape you build. Tangrams help you practice recognizing triangles, squares, and parallelograms while developing spatial reasoning skills.
Worked Example
Problem: A tangram square has a side length of 8 cm. Find the area of one small triangle.
Step 1: Find the total area of the square.
Step 2: A standard tangram divides the square into 16 equal small-triangle units. Each of the two small triangles equals 1 unit, the medium triangle equals 2 units, the square equals 2 units, the parallelogram equals 2 units, and each large triangle equals 4 units. Check: 1 + 1 + 2 + 2 + 2 + 4 + 4 = 16 units.
Step 3: Each small triangle covers 4 cm² of the total area.
Answer: One small triangle has an area of 4 cm².
Another Example
Problem: Using the same 8 cm tangram square, find the area of one large triangle.
Step 1: Recall the total area is 64 cm² and a large triangle occupies 4 out of 16 equal units.
Step 2: Simplify the fraction and multiply.
Answer: One large triangle has an area of 16 cm².
Visualization
Why It Matters
Tangrams are widely used in elementary math classes to teach shape recognition, area, fractions, and symmetry through hands-on exploration. Working with the seven pieces builds spatial reasoning, a skill that supports later success in geometry and even fields like architecture and engineering. Many standardized math curricula from kindergarten through grade 5 include tangram activities.
Common Mistakes
Mistake: Using only some of the seven pieces to form a shape.
Correction: A proper tangram figure must use all seven pieces with no gaps and no overlaps. If a piece is left over, the solution is not complete.
Mistake: Forgetting that the parallelogram can be flipped (reflected) while the other pieces only need rotation.
Correction: The parallelogram is the only tangram piece that is not symmetric, so you sometimes need to flip it over to make it fit. The triangles and square look the same on both sides.