### Theory:

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

Therefore, we can derive the area of a circular pathway as below.

$\begin{array}{l}=\mathrm{\pi }{R}^{2}-\mathrm{\pi }{r}^{2}\\ \\ =\mathrm{\pi }\left({R}^{2}-{r}^{2}\right)\phantom{\rule{0.147em}{0ex}}\mathit{sq}.\phantom{\rule{0.147em}{0ex}}\mathit{units}\end{array}$
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 $\mathrm{\pi }{r}^{2}$.
• Circumference of the circle is $2\mathrm{\pi }r$.
• Here $$r$$ is the radius of the circle.