Main Concept

Consider a circle being divided into pie slices, or sectors. The circle's area can be easily visualized by rearranging these sectors to form a rectangle. We use the formula Area = Length x Width, and approximate the length of the rectangle to be half of the circumference, where the circumference is given by $\mathit{2}\mathit{\cdot }\mathrm{\π}\mathit{\cdot }$Radius. Combining these two formulae, the area is given by $\left( \mathrm{\π}\cdot r\right)\cdot \left(r\right) \= \mathrm{\π}\cdot r^2$. Although we use only approximations for the length and width, the resulting formula for the circle's area is exact.

Number of Sectors:  

More MathApps

MathApps/Trigonometry