Question : The perimeter of a sector of a circle of radius 7.4 cm is 20.6 cm. The area of this sector is:
Option 1: 42.92 cm2
Option 2: 5.8 cm2
Option 3: 10.73 cm2
Option 4: 21.46 cm2
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Correct Answer: 21.46 cm 2
Solution :
The radius of the circle = 7.4 cm
Let the length of the arc be $l$ cm.
The perimeter of the sector = Radius + Length of the arc + Radius
$⇒20.6 = 7.4 + l + 7.4$
$⇒l = 20.6 -14.8 = 5.8$ cm
Area = $\frac{1}{2} ×\text{ length of arc × radius}$
$=\frac{1}{2}\times 5.8\times 7.4=21.46$ cm$^2$
Hence, the correct answer is 21.46 cm
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