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**scherz0** Hello everyone,

I fully understand the idea behind the formula for the area of a sector of a circle with angle $\displaystyle \theta $:

$\displaystyle \text{Area of a sector of a circle}=\frac{\theta }{2\pi }\left( \pi {{r}^{2}} \right) \text{ (*) } , $

$\displaystyle \text{where }\frac{\theta }{2\pi }\text{ gives the specific ''slice'' of the circle} $

$\displaystyle \text{and }\pi {{r}^{2}}=\text{area of the circle}\text{.} $

However, I am having trouble interpreting the simplified form of this formula:

$\displaystyle \text{Area of a sector of a circle} = \frac{1}{2} \pi r^2 $.

What does it mean to multiply the angle of the sector by the radius squared, and then dividing this by half? How can this be interpreted to give us the area of a sector of a circle, WITHOUT referring to the original expression $\displaystyle \text{ie (*)} $

Thank you very much.