Question
Find the area (in cm²) of the sector whose perimeter is
is 64/3 cm and central angle is 60°. (Use π = 22/7.)Solution
Perimeter of sector = Arc length + 2 × Radius = 64/3 cm Central angle (θ) = 60° Let radius = r cm. Arc length (L): = 60°/360° × 2πr =1/6 × 2 × 22/7 × r=22r/21 Perimeter equation: 22r/21 + 2r = 64/3 Multiply by 21: 22r + 42r = 448 ⟹ 64r = 448 ⟹ r = 7 cm Area of sector: 60°/360° × πr2 =16 × 22/7 × 49 = 77/3 cm2
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