Скачать или смотреть Reuleaux Triangle Area Explained - Circle Geometry Problem with π

Finding the area of the curved region between three mutually tangent unit circles.
Solution:

Connect the centers of the three circles to form an equilateral triangle
Each side of the triangle = 1 + 1 = 2 (sum of two radii)
Area of equilateral triangle = (√3/4) × 2² = √3
Each 60° sector area = (60/360) × π × 1² = π/6
Total area of three sectors = 3 × π/6 = π/2
Curved region area = Triangle − Sectors = √3 − π/2 ≈ 0.161

Formulas used:

Equilateral triangle area = (√3/4) × side²
Sector area = (θ/360°) × πr²

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