Suppose the small square has area one square unit:
The two small congruent triangles make a square congruent to the one above, which has area one square unit:
Since the small square has area one square unit, each of the triangles must have area one-half square unit:
This is a parallelogram:
Each of the triangles has area one-half square unit, so the parallelogram must have area one square unit:
This is the medium-size triangle:
Each of the triangles has area one-half square unit, so the medium-size triangle must have area one square unit:
This is a large triangle:
Since the small square has area one square unit and each of small triangles has area one-half square unit, the large triangle must have area two square units:
Since each large triangle has area two square units, the large square must have area four square units:
Areas of Tangrams (answer
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