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Moderate

Relating Perimeter to Area

GMAT-ONFGNG

A given sector in a circle has arc length equal to an unknown value $x$. Assume the radius of the circle is $ y$ and the sector's central angle is $ \theta $.

What is the area of the sector in terms of $x$, $y$, and $ \theta $?

A

$ \cfrac{y\theta(x-2y)}{360} $

B

$ (x-2y)(\cfrac{y}{2}) $

C

$ \cfrac{\theta}{360}\times{\pi(y^{2})} $

D

$ \cfrac{x-2y}{y^2} $

E

None of the answers is correct.