A) \[\frac{\pi }{\sqrt{3}}{{a}^{2}}\]
B) \[\frac{\pi {{a}^{2}}}{16}\]
C) \[\frac{\left( \pi -\sqrt{2} \right)}{4}{{a}^{2}}\]
D) \[\frac{2\sqrt{3}}{\pi }{{a}^{2}}\]
Correct Answer: B
Solution :
(b): Area = larger semicircle \[-2\times \] smaller semicircles \[=\frac{1}{2}\left[ \frac{\pi {{a}^{2}}}{4}-2\times \frac{\pi }{4}{{\left( \frac{a}{2} \right)}^{2}} \right]=\frac{1}{2}\times \frac{\pi {{a}^{2}}}{4}\left( 1-\frac{1}{2} \right)=\frac{\pi {{a}^{2}}}{16}\]
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