### 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.

$\begin{array}{l}=\mathrm{\pi}{R}^{2}-\mathrm{\pi}{r}^{2}\\ \\ =\mathrm{\pi}({R}^{2}-{r}^{2})\phantom{\rule{0.147em}{0ex}}\mathit{sq}.\phantom{\rule{0.147em}{0ex}}\mathit{units}\end{array}$

- 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.

Important!

**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.