### Theory:

The fundamental idea about the area of pathways
• We should observe the circular shapes around us where we need to find the area of the pathway.
• The area of the pathway is the difference between the area of the outer circle and inner circle.
• Let ‘$$R$$’ be the radius of the outer circle, and ‘$$r$$’ be the radius of the inner circle.
Therefore, the area of the circular pathway,

$\begin{array}{l}=\mathrm{\pi }{R}^{2}-\mathrm{\pi }{r}^{2}\\ \\ =\mathrm{\pi }\left({R}^{2}-{r}^{2}\right)\phantom{\rule{0.147em}{0ex}}\mathit{sq}.\phantom{\rule{0.147em}{0ex}}\mathit{units}\end{array}$
Important!
• The circle is a round plane figure whose boundary (the circumference) consists of points equidistant from the fixed point (the centre).
• Area of the circle is the region enclosed by the circle.
• Distance around the circular region is called the circumference or perimeter of the circle.
Recollect the formula:

Area of the circle is $\mathrm{\pi }{r}^{2}$
Here $$r$$ is the radius of the circle.

Circumference of the circleis$2\mathrm{\pi }r$
Here $$r$$ is the radius of the circle.