Half the figure is two pieces
All seven standard tangram pieces together have the area of sixteen small triangles. Each big triangle has the area of four small ones, so the two big triangles cover half the total area.
Trying the big triangles first can help you organize a large part of the outline. It is a strategy, not a rule: a distinctive corner or notch may suggest another piece first.
In this square example, place the big triangles, then the middle triangle, the square and the parallelogram. The small triangles fill the remaining gaps.
The square, in order
Start with the square figure. The two big triangles fill the half of the square below one diagonal. They meet along a line from the center to a corner.
The middle triangle, the square and the parallelogram go in next and leave two triangular gaps.
The two small triangles fill those gaps, and the tray is full.
Compare the areas
The same square is empty again.
Each big triangle has the area of four small triangles. All seven pieces together have the area of sixteen. What part of the square will the two big triangles cover without overlapping?
Try it
What fraction of the square do the two big triangles cover together?
- A half (1/2)
- A quarter (1/4)
Show the answer
A half (1/2)
Together they cover half the square: 4 + 4 = 8 small-triangle units out of 16, so 8/16 = 1/2.
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