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A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below

What is the area of the shaded part of the circle? 

(a) 2π cm2

(b) 4π cm2 

(c) 5π cm2 

(d) 10π cm2

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Correct answer is (d) 10π cm2

Explanation: The area of the circle is = πr2 = π52 = 25 πcm2

The area of the pentagon is 5 x (1/2 x s x h) = 5 x (1/2 x 4.33 x 2.5) = 5 x 5.4125 = 27.0625 cm2

Therefore, the area of the shaded part of the circle is 25 π cm2 - 27.0625 cm2 = 10 π cm2

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