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Q.

In Fig., ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a

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Detailed Solution

here, we have to find the area of semicircle ,

In triangle ABC 

By using Pythagoras

Let the radius are, 

AB = AC = 14 cm 

Using  Pythagoras theorem, we can find the hypotenuse (BC) of ΔABC.

BC2 = AB2 + AC2

= (14)2 + (14)2

BC = 2 × (14)2

= 142 cm

Therefore, The radius of semicircle BDC, r = BC/2 = 142/2 = 72 cm

Area of the shaded region = Area of semicircle - (Area of quadrant ABC - Area ΔABC)

πr2/2 - [900/3600 × π(14)2 - 1/2 × AC × AB]

π(72)2/2 - [π(14)2/4 - 1/2 × 14 × 14]

= [(22 × 7 × 7 × 2)/(7 × 2)] - [(22 × 14 × 14)/(7 × 4) - 7 ×14]

= 154 - (154 - 98)

= 98 cm2

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