Tangram Shape Puzzle
Drag, turn and flip the seven classic tangram pieces to fill 38 outlines. Every outline really can be made — each one was solved by the computer before it was added.
A tangram is one square cut into seven pieces — five triangles, a square and a parallelogram — rearranged to make a picture with no gaps and no overlaps. Taking the smallest triangle as 1 unit, the square, parallelogram and medium triangle are 2 units each and each large triangle is 4, so the set is 16 small triangles.
Choose an outline
Green dot = easy, yellow = medium, red = tricky.
The seven pieces — names, angles and area
Lengths are given in “units”, where 1 unit is the short side of the smallest triangle. Put together, the seven pieces make a square of side 2√2 ≈ 2.83 units and area 8 units².
Three discoveries to make with the pieces
Join the two small triangles along their long sides and you get the square. Join them along a short side and you get the medium triangle. Slide one along and you get the parallelogram. All three have the same area — 1 unit².
Area 2 units² against ½ unit² — so one large triangle covers four small triangles exactly. That makes the whole set worth 16 small triangles, and each large triangle is a quarter of the finished square.
Six pieces have a mirror line, so a flip looks the same as a turn. The parallelogram does not — it is chiral. If a puzzle will not close up, flip the parallelogram.
| Piece | How many | Angles | Area (units²) | Share of the square |
|---|---|---|---|---|
| All seven | 7 | — | 8 | 100% |
Tangram pieces to cut out
Cut along every line. The seven pieces make this square again — and 38 more shapes. ClassHud Tools · classhud.com
Name: ______________________________ Class: __________ Date: ____________
Seven pieces, thirty-eight shapes
A tangram is one square cut into seven pieces. Rearranged — never overlapping, never leaving a gap — those same seven pieces become a cat, a boat, a rocket or a letter T.
Pick an outline
Start with an easy one (green dot). The dark shape is exactly the area of all seven pieces.
Drag a piece in
Pieces snap to each other and to the outline, so near enough is good enough.
Turn and flip
Turn in 15° steps; let go and it clicks to the nearest 45°. Only the parallelogram ever needs flipping.
Fill it completely
When the outline is covered with nothing sticking out, the puzzle is solved.
Why tangrams teach geometry
Children handle right angles, 45° angles, congruence and area without a single formula. Two small triangles making one square is a proof of ½ + ½ = 1 that you can see and feel.
Matches the NCERT Class 3–6 work on shapes, symmetry and area by counting.
The three triangle sizes
All five triangles are the same shape — right-angled and isosceles, angles 45°, 45°, 90°. Only their size changes: legs of 1, √2 and 2 units, so their areas are ½, 1 and 2. That is a first look at similar figures: double the sides, four times the area.
Area without measuring
Take the small triangle as one “bit”. Then the medium triangle and the square and the parallelogram are 2 bits each, and each large triangle is 4 bits. The whole square is 2(1) + 2 + 2 + 2 + 2(4) = 16 bits — so a large triangle is ¼ of the square and a small one is 1/16.
Where tangrams come from
The puzzle appeared in China around 1800 and reached India and Europe within twenty years. Its Chinese name, qi qiao ban, means “seven boards of skill”. The seven pieces have never changed.
Tangram Shape Puzzle — your questions
What are the seven tangram pieces?
Two large triangles, one medium triangle, two small triangles, one square and one parallelogram. All five triangles are right-angled and isosceles with angles of 45°, 45° and 90° — only their size changes. Together the seven pieces form a square, which is why a tangram is sometimes called the seven boards of skill.
What is the area of each tangram piece?
Take the small triangle as 1 unit. The medium triangle, the square and the parallelogram are each 2 units, and each large triangle is 4 units. The complete set is 2(1) + 2 + 2 + 2 + 2(4) = 16 units, so a large triangle is a quarter of the whole square and a small triangle is one-sixteenth.
Why does one tangram piece need to be flipped over?
Six of the pieces have a line of symmetry, so turning one over looks exactly the same as rotating it. The parallelogram does not — it is chiral, meaning its mirror image cannot be reached by turning. If a puzzle will not close up and everything else looks right, flip the parallelogram.
How do you make a square with tangram pieces?
Put the two large triangles together along their long sides to make the top half of the square, then fill the bottom half with the medium triangle, the square, the parallelogram and the two small triangles. Starting from the biggest pieces is the general rule for every tangram outline.
What do tangrams teach in maths?
Children handle right angles, 45° angles, congruence, similarity and area without a single formula. Joining two small triangles makes the square, the medium triangle or the parallelogram — three different shapes of equal area — which is a proof of half plus half equals one that you can see and feel.
Where did the tangram come from?
The puzzle appeared in China around 1800 and reached India and Europe within about twenty years. Its Chinese name, qi qiao ban, means seven boards of skill. The seven pieces and their proportions have never changed since, which is why a tangram set from anywhere in the world fits the same outlines.