Question

In the given figure the diameter of the largest semicircle is 14 cm. Three semicircles are drawn with AK, KM and MB as diameter, where AK=KO=OM=MB and AK+KO+OM+MB=AB. Find the area of the shaded region. (4)

Answer 1

Answer:

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Answer 2

Answer:

$\frac{385}{8} {cm}^{2}$

Step-by-step explanation:

I can't get the diagram for this question. so, I assumed a figure based on the given details.

we know that, area of semi circle = (π×d²)/8 where, d is the diameter of semi circle.

area of shaded region = area of AB - (area of AK + area of KM + area of MB)

$= \frac{\pi}{8} \times {14}^{2} - (( \frac{\pi}{8} \times {7}^{2} ) + ( \frac{\pi}{8} \times { \frac{7}{2} }^{2} ) + ( \frac{\pi}{8} \times { \frac{7}{2} }^{2} )) \\ = \frac{22}{7} \times \frac{1}{2} \times (49 - \frac{49}{4} - \frac{49}{16} - \frac{49}{16} \\ = \frac{385}{8}$