Multiple choice

The perimeter of a sector of circle of radius 5.2 cm is 16.4 cm. Find the area of the sector.

  1. 15.6 cm2

  2. 14.9 cm2

  3. 16.6 cm2

  4. 20.4 cm2
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A Correct answer
Explanation

Perimeter of a sector = r + r + arc_length = 2r + (θ/360 × 2πr). Given 16.4 = 2(5.2) + arc_length, so arc_length = 16.4 - 10.4 = 6 cm. Angle θ = (6 × 360)/(2 × π × 5.2) ≈ 66.3°. Area = (θ/360) × πr² = (66.3/360) × π × 27.04 ≈ 15.6 cm².

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