| In the given figure, ABCD is a trapezium with \[AB||CD\]. The area of the shaded region is: |
 |
A) \[3\pi \,c{{m}^{2}}\]
B) \[6\pi \,c{{m}^{2}}\]
C) \[9\pi \,c{{m}^{2}}\]
D) \[7\pi \,c{{m}^{2}}\]
Correct Answer: A
Solution :
| [a] Since \[AB||CD\] and AD is transversal |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\angle A+\angle D=180{}^\circ \] |
| (Sum of angles on the same side of transversal is \[180{}^\circ \]) |
| Now, \[r=3cm,\] \[\theta =120{}^\circ \] |
| \[\therefore \] Area of shaded sector |
| \[=\frac{\pi {{r}^{2}}\theta }{360{}^\circ }=\pi \times 3\times 3\times \frac{120{}^\circ }{360{}^\circ }\] |
| \[=3\pi \,c{{m}^{2}}\] |
| Hence, area of shaded region is \[3\pi c{{m}^{2}}\]. |
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