Multiple choice

If the perimeter of a sector of a circle of radius $5.6\ cm$ is $27.2\ cm$, then the area of the sector is

  1. $16\ cm^{2}$
  2. $27.2\ cm^{2}$
  3. $42.8\ cm^{2}$
  4. $44.7\ cm^{2}$
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D Correct answer
AI explanation

The perimeter of a sector equals the sum of two radii plus the arc length, so 27.2 = 2(5.6) + arc length, giving an arc length of 16 cm. The area of the sector is calculated as 0.5 * radius * arc length. Substituting the values gives 0.5 * 5.6 * 16, which equals 44.7 cm squared.

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