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 shded region ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 394.24
Let OD = x = radius of circle
OF = (28 - x)
OM = (x + 7)
Now, applying pythogoras theorem
(7 + x)2 = 72 + (28 - x)2
⇒ x2 + 14x + 49 = 49 + 784 + x2 - 56x
⇒ 70x = 784
⇒ x = 11.2
Area of circle = πr2 = π × (11.2)2
= 394.24 cm²