The perimeter of the circular field is 242 cm. The area of the field is ___.

The perimeter of a circle is also known as the circumference and is calculated using the formula ⁠⁠⁠⁠⁠⁠⁠$2\mathrm{\pi r}$, where r is the radius of the circle.

Given,

The perimeter of the circular field is 242 cm.

The perimeter of the circular field $=2\mathrm{\pi r}$

$2\mathrm{\pi r}=242$

$\mathrm{r}=\frac{242}{2\times {\displaystyle \frac{22}{7}}}=\frac{242\times 7}{44}=\frac{77}{2}$

The area of a circular field $={\mathrm{\pi r}}^2$

$=\frac{22}{7}\times \frac{77}{2}\times \frac{77}{2}=4658.5 {\mathrm{cm}}^2$

Therefore, the area of a circular field is 4658.5 cm².