A sector has arc length $l$ and radius $r$. Which expression gives its area?
A$A=lr$
B$A=\dfrac{l}{2r}$
C$A=\dfrac{1}{2}lr$
D$A=2lr$
Answer & Solution
Correct answer: C. $A=\dfrac{1}{2}lr$
The relation between sector area and arc length is $A=\dfrac{1}{2}lr$. This is consistent with the standard formulas $l=\dfrac{\pi r\theta}{180}$ and $A=\dfrac{\pi r^2\theta}{360}$, because substituting $l$ into $\dfrac{1}{2}lr$ gives the same area formula. The other options either miss the factor $\dfrac{1}{2}$ or have incorrect dimensions.
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