A field is in the form of a circle. The cost of fencing around it at ₹12 per metre is ₹2,640. What is the area (in m$^2$) of the field? (Take $\pi = \frac{22}{7}$)

3850 $m^2$

We know that,

Area of circle = πr² 

Perimeter of circle = 2πr

Cost of 1 m fencing = Rs. 12 per metre

Total length of fencing = \(\frac{2640}{12}\) = 220 m

Perimeter of circle = 220

Now according to the question,

2πr = 220

2 × \(\frac{22}{7}\) × r = 220

r = 35

Area of circle = πr² = \(\frac{22}{7}\) × 35 × 35 = 3850 m²