A) \[\frac{1}{2}lr\]
B) \[lr\]
C) \[\frac{1}{3}lr\]
D) \[\frac{1}{2}l{{r}^{2}}\]
Correct Answer: A
Solution :
| The area of sector is given by \[A=\frac{\theta }{360}\times \pi {{r}^{2}}\]and length of the arc is given by \[l=\frac{\theta }{360}\times 2\pi \] |
| Multiplying and dividing A by 2, we get |
| \[A=\frac{1}{2}\times \frac{\theta }{360}\times 2\times \pi {{r}^{2}}=\frac{1}{2}\times \left( \frac{\theta }{360}\times 2r \right)\times r=\frac{1}{2}\times l\times r\]So, option [a]is correct. |
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