The cost of fencing a square lawn at Rs 14 per metre is Rs 2800.

Given:
Cost of fencing = Rs 2800
Rate of fencing = Rs 14

Now,

Perimeter $=\frac{\text { Total cost }}{\text { Rate }}=\frac{2800}{14}=200 \mathrm{~m}$

Because the lawn is square, its perimeter is $4 a$, where $a$ is the side of the square).

$\Rightarrow 4 a=200 \Rightarrow a=\frac{200}{4}=50 \mathrm{~m}$

Area of the lawn $=\mathrm{Side}^{2}=50^{2}=2500 \mathrm{~m}^{2}$

Cost for mowing the lawn per $100 \mathrm{~m}^{2}=$ Rs 54

Cost for mowing the lawn per $1 \mathrm{~m}^{2}=\mathrm{Rs} \frac{54}{100}$

Total cost for mowing the lawn per $2500 \mathrm{~m}^{2}=\frac{54}{100} \times 2500=$ Rs 1350