Tangram shapes

Tangram shapes with 7 pieces

Looking up tangram shapes with 7 pieces? The classic set is five right triangles, one square and one parallelogram cut from a single square. Here is every tan with its name, picture, area ratio, and flip tips—then links to play online or print worksheets with answers.

All 7 pieces as one square

This is the classic rebuilt square—every tan labelled. The two large triangles (LT) meet along a diagonal; the square (SQ) and parallelogram (PR) share the mid-size area with the medium triangle (MT); the two small triangles (ST) fill the remaining corners.

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Each tangram piece, one by one

Large triangle × 2

Large triangle · code LT

Two congruent isosceles right triangles. Each has legs of length 2√2 when the whole set forms a square of side 4, so each large tan covers a quarter of that square.

Tip: Park these first on big corners or long hypotenuses of a silhouette. Leaving both large triangles for last almost always leaves an awkward L-shaped gap.

Flip / turn: Flipping does not create a new outline for an isosceles right triangle, but 45° turns do—use Turn until the hypotenuse matches the silhouette edge.

area 4×2 in set

Medium triangle × 1

Medium triangle · code MT

One isosceles right triangle whose legs are length 2. Its area is half of a large triangle (or twice a small triangle).

Tip: Often bridges a large triangle and a smaller pocket. If a mid-size right-angle notch remains, try the medium triangle before the square.

Flip / turn: Same as the large triangles: rotate in 45° steps; flip is optional for feel, not for a new shape.

area 2×1 in set

Small triangle × 2

Small triangle · code ST

Two congruent isosceles right triangles with legs of length √2. Each covers one-sixteenth of the classic square—the smallest area unit in the set.

Tip: Save at least one small triangle for fiddly leftover corners. Two small triangles can rebuild the medium triangle’s area, which helps when checking pockets mentally.

Flip / turn: Rotate freely; together they often finish a diamond or a thin tip of an animal silhouette.

area 1×2 in set

Square × 1

Square · code SQ

A square with side √2. Area equals one medium triangle (two small triangles). At 0° it sits flat; at 45° it becomes a diamond on the board.

Tip: Look for a right-angle pocket whose side matches the square. If the pocket is diamond-shaped, turn once (45°) before forcing a triangle into it.

Flip / turn: Flip does not change the square’s outline. Only two distinct looks matter in practice: axis-aligned and diamond.

area 2×1 in set

Parallelogram × 1

Parallelogram · code PR

A parallelogram (sometimes called a rhomboid) with base √2 and a 45° slant. Same area as the medium triangle and the square.

Tip: This is the piece that most often needs a Flip. If edges almost match but lean the wrong way, flip before you keep turning.

Flip / turn: The mirror image is a different placement. On PuzzlePave’s board, select the parallelogram and press Flip (or F) when a 45° edge refuses to line up.

area 2×1 in set

Colours match the free online board. Area is measured in small-triangle units (ST = 1).

How the classic 7-piece square is cut

Start with one square. Slice it so you keep two large congruent isosceles right triangles, one medium triangle similar to them, two small triangles also similar, one square, and one parallelogram. Nothing is left over: the seven areas add up to the original square. That dissection is what people mean by tangram shapes with 7 pieces—not a random set of polyominoes.

PuzzlePave uses the traditional proportions on a unit square of side 4 (area 16). In those units, each large triangle has area 4, the medium triangle, square and parallelogram each have area 2, and each small triangle has area 1. Counting by “small-triangle units” makes mental checks easy while you solve: every closed pocket must be fillable with a sum of 1s, 2s and 4s from the tans you still hold.

Piece	Count	Area units	Share of square
Large triangle	×2	4 each	50%
Medium triangle	×1	2 each	13%
Small triangle	×2	1 each	13%
Square	×1	2 each	13%
Parallelogram	×1	2 each	13%
All 7 tans	7	16	100%

Symmetry, turns and flips

On our board every tan turns in 45° steps. That matches wooden tabletop sets where edges often meet at half-right angles. Triangles and the square keep the same outline when flipped over; the parallelogram does not. If a silhouette edge leans the “wrong” way, Flip the parallelogram before you assume the puzzle is broken.

Large / medium / small triangles: rotate until a leg or hypotenuse hugs the outline; flip is optional.
Square: two useful looks—flat (0°) and diamond (45°).
Parallelogram: treat Flip as a first-class move; many animal and boat outlines need the mirror.
Never cover the silhouette with only six pieces—every level on PuzzlePave uses the full set of seven.

Strategy that follows from the ratios: place both large triangles early, park the square when you see a matching pocket, then decide whether the parallelogram or the medium triangle owns the long 45° edge. Finish with the small triangles. Our free tangram puzzle online encodes that same set on every level, with Hint placing one tan from a real solution when you stall.

Practice on screen or on paper

Want to feel the shapes with your fingers? Open the tangram printable PDF page: cut-out tans, silhouette worksheets and an answer key, printed via your browser’s Print / Save as PDF—no third-party file host. Prefer the screen? Play tangram online free (English) or 七巧板在线 (Chinese)—same seven wooden tans, touch-first controls, local progress.

Coming from square-grid packing? Compare with pentomino shapes (twelve 5-square letters) or the polyomino puzzle. Tangrams are continuous dissections, not grid polyominoes, but the same habit helps: protect connected empty space and check area before forcing a piece.

FAQ

How many tangram shapes are there with 7 pieces?

A classic tangram always uses exactly seven tans: two large triangles, one medium triangle, two small triangles, one square and one parallelogram. Together they rebuild one square and thousands of other silhouettes.

What are the names of the 7 tangram pieces?

Large triangle (×2), medium triangle (×1), small triangle (×2), square (×1) and parallelogram (×1). PuzzlePave labels them LT, MT, ST, SQ and PR in diagrams.

What are the area ratios of tangram pieces?

Count in small-triangle units: each small triangle = 1, medium triangle = square = parallelogram = 2, each large triangle = 4. The seven pieces total 16 units—the area of the classic square.

Which tangram piece do you flip?

The parallelogram. Triangles and the square look the same when flipped over; the parallelogram’s mirror leans the other way and is required for many outlines.

Can the 7 tangram pieces make a square?

Yes—that is the defining dissection. Level 1 of our free tangram game is that classic square, built from a verified placement of all seven tans.

Where can I print tangram shapes with answers?

Use PuzzlePave’s free tangram printable: cut-out tans, silhouette worksheets and an answer key. Print or Save as PDF—no download of a third-party file and no sign-up.