The tangram
Cut a square along the lines shown. You get seven flat pieces. Put them back in the square. Each piece you place shows its share.
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- Start with a square.
- Cut the diagonal. Cut one half in two.
- Cut a corner off the other half.
- Cut the rest in four. Each piece has a share.
The rule
A tangram is a square cut into seven pieces. Two big triangles are 1/4 each. The medium triangle is 1/8. So are the little square and the slanted piece. Two small triangles are 1/16 each. The shares add to 1.
Count in small triangles. A medium triangle equals 2 of them. The whole square equals 16. So 2 of 16 is 1/8. The slanted piece (a parallelogram) equals 2 as well. A parallelogram has two pairs of parallel sides.
Every figure made with all seven pieces uses the same total area. That area equals the area of the square.
Example: the two big triangles are 4 + 4. The medium triangle, little square and slanted piece are 2 + 2 + 2. The two small triangles are 1 + 1. In all, 4 + 4 + 2 + 2 + 2 + 1 + 1 = 16 small triangles.