A) \[\left( 102\frac{2}{3}-49\sqrt{3} \right)c{{m}^{2}}\]
B) \[\left( 103\frac{2}{3}-4998\sqrt{3} \right)c{{m}^{2}}\]
C) \[\left( 109-38\sqrt{3} \right)cm\]
D) None of these
Correct Answer: A
Solution :
(a): Area of triangle \[\text{ABC}=\frac{\sqrt{3}}{4}\times {{(14)}^{2}}\] \[=49\sqrt{3}c{{m}^{2}}\] Area of sector \[\text{ABC}=\pi \times {{(14)}^{2}}\times \frac{60}{360}\] \[=102\frac{2}{3}c{{m}^{2}}\] Area of shaded region \[=\left( 102\frac{2}{3}-49\sqrt{3} \right)c{{m}^{2}}\]
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