# In the given figure, AB, AE, EF, FG, and GB are semicircles. AB = 56 c

| 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 cm

^{2}) of the shaded region?A. 414.46

B. 382.82

C. 406.48

D. 394.24

### Right Answer is: D

#### SOLUTION

Let the radius of the shaded circle be x and centre is O.

OP = 7 + x

OF = 28 – x

PF = 7 cm

In triangle OFP,

(7 + x)^{2} = (28 – x)^{2} + 7^{2}

x = 11.2 cm

Required Area = (22/7) × 11.2 × 11.2 = 394.24 cm^{2}

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In the given figure, AB, AE, EF, FG, and GB are semicircles. AB = 56 c