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The area of the square field is one hectare.

So, the area of the square field in \[{{\text{m}}^2}\],

\[

= 6 \times 10000 \\

= 60000{{\text{m}}^2} \\

\]

[One hectare is equals to \[10000{\text{ }}{{\text{m}}^2}\]]

The area that has to be covered is \[6\] kilometers.

So, the area that has to be covered in \[{\text{m}}\],

\[

= 6 \times 1000 \\

= 6000{\text{m}} \\

\]

[One kilometer is equals to \[1000{\text{ m}}\]]

As we know that the sides of the square are of the same length.

Let the length of the sides of the square is \[x\].

The area of the square field is:

\[

{\text{A}} = {{length \times breadth}} \\

60000 = x \times x \\

60000 = {x^2} \\

\sqrt {60000} = x \\

\pm 244.94 = x \\

\]

As we know that the length of the sides cannot be negative so it will be positive. So,the length of side of the square is \[ + 244.94{\text{ m}}\].

The perimeter of the square is:

\[

= 4 \times {\text{length of sides}} \\

= 4 \times 244.94 \\

= 979.76{\text{ m}} \\

\]

The number of times I must run around a square field:

\[

= \dfrac{{{\text{The total area to be covered}}}}{{{\text{The perimeter of the square}}}} \\

= \dfrac{{6000}}{{979.76}} \\

= 6.12 \\

\]

In these types of questions, calculate perimeter whenever asked for distance traveled or length. Use basic formulas of area and perimeter. And always convert the units to make the calculations easy.