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This question belongs to Arithmetic Ability Mensuration 2D
Mensuration 2D
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In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in cm2) of the shaded region?
Mensuration 2D mcq question image

Answer & Solution
Correct Answer: Option D
Mensuration 2D mcq question image
AB = 56 cm
AE = EF = FG = GB = 14 cm
∴ EM = MF = 7 cm
PF = $$\frac{{56}}{2}$$ = 28 cm
OF = 28 - r
OM = 7 + r
MF = 7
In ΔOMF,
OM2 = OF2 + MF2
(7 + r)2 = (28 - r)2 + 72
49 + r2 + 14r = 784 + r2 - 56r + 49
70r = 784
r = $$\frac{{784}}{{70}}$$ = 11.2
Area of circle = πr2
= $$\frac{{22}}{7} \times \frac{{112}}{{10}} \times \frac{{112}}{{10}}$$
= 394.24 cm2
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