In the given figure, AB is a diameter of the largest semi-circle. AB=21cm . . .

Question : In the given figure, AB is a diameter of the largest semi-circle. AB=21cm, AM=MN=NB. Semicircles are drawn with AM, MN and NB as diameters as shown. What is the area of the shaded region? Use π=22/7

a) 105 cm²

b) 210.5 cm²

c) 192.5 cm²

d) 225 cm²

Doubt by Saumya S.

Solution :
 

AB = 21 cm 

AM=MN=BN = 21/3 = 7 cm

Radius of bigger semi circle (R) = 21/2 cm
Radius of small semi circle (r) = 7/2 cm

Area of shaded region 

= Area of bigger semicircle of Radius R - area of semi circle of radius r + 2× area of small semi circle of radius r

= πR²/2 - πr²/2 + 2πr²/2
= πR²/2 + πr²/2 
= π/2 [R²+r²]

= (22/7)×(1/2) [(21/2)²+(7/2)²]
= (11/7)×[441/4+49/4]
= (11/7)×[490/4]
= (11×70)/4
= 770/4
= 192.5 cm²

Hence, c) would be the correct option.