- Arc length = (m/360) * C, where m is the central angle measure and C is the circumference.
- Area of sector = (m/360) * πr², where m is the central angle measure and r is the radius.
- For Example 1a: Given circle P, ∠APC = 120°, radius = 4. Arc length ABC = (120/360) * π * 8 = (1/3)(8π) = 8π/3 units.
- For Example 1b: Area of shaded sector = (120/360) * π * 4² = (1/3) * π * 16 = 16π/3 units².
- For Example 2: Given circle P, ∠APB = 60°, radius = 6. Area of segment = area of sector minus area of triangle.
- Sector area = (60/360) * π * 6² = (1/6) * π * 36 = 6π.
- Triangle area = (6² * √3)/4 = (36 * √3)/4 = 9√3.
- Segment area = 6π - 9√3 units².
Parent Tip: Review the logic above to help your child master the concept of geometry worksheet arc length sector area segment area.
