🔺 Tangram Math Explorer 🔺

📐 Mathematical Properties

Area Relationships

Total Area = 1 unit²

• Large triangles: 1/4 each
• Medium triangle: 1/8
• Small triangles: 1/16 each
• Square: 1/8
• Parallelogram: 1/8

Geometric Concepts

• Right triangles
• Isosceles triangles
• 45-45-90 triangles
• Congruent shapes
• Similar triangles
• Area conservation

🧮 Math Challenges

Challenge 1: Fraction Fun

If the total tangram area is 1, what fraction represents combining both large triangles?

Answer: 1/4 + 1/4 = 2/4 = 1/2 of the total area

Challenge 2: Ratio Reasoning

What's the ratio of a large triangle's area to a small triangle's area?

Answer: (1/4) ÷ (1/16) = 4:1 ratio

Challenge 3: Perimeter Puzzle

If the square has a side length of 1 unit, what's the perimeter of the entire tangram square?

Answer: 4√2 + 4 ≈ 9.66 units

🎯 Learning Activities

Beginner Level

• Count vertices and sides
• Identify shape types
• Compare areas visually
• Practice basic fractions

Advanced Level

• Calculate exact areas
• Find angle measures
• Explore transformations
• Create algebraic expressions

🔄 Interactive Controls

💡 Math Hints

• All pieces together form a perfect square

• The diagonal of the square piece equals the side of small triangles

• Tangrams demonstrate conservation of area through transformation