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**Hint:**We are given that Parminder walks around a square park and covers a distance of \[800m\]. We are asked to find the area of the park. We will first have to find the side of the square shaped park. We are given that when Parminder moved around the park, in a way telling us that the perimeter of the park is \[800m\]. We know that the perimeter of the square is, \[4\times side\]. We will equate the perimeter to \[800m\] and we will get the value of the side. Then the area can be found by the formula, \[{{\left( side \right)}^{2}}\]. Hence, we will have the area of the square park.

**Complete step by step answer:**

According to the given question, we are given that Parminder walked around a square park and covered a distance of \[800m\] and we are asked to find the area of the park.

We are given the distance covered by Parminder along the sides of the park, in short, we are given the perimeter of the square park.

We know that the formula of the perimeter of a square is \[4\left( side \right)\]

So, equating the values, we get,

\[4s=800\]

Now, writing the expression in terms of side, we get,

\[\Rightarrow s=\dfrac{800}{4}\]

\[\Rightarrow s=200m\]

So, we get the value of the side = \[200m\]

In order to find the area of the square park and we will use the formula of the area of a square, which is,

\[Area={{\left( side \right)}^{2}}\]

We will now substitute the values in the above expression and we get,

\[\Rightarrow Area={{\left( 200 \right)}^{2}}\]

\[\Rightarrow Area=40000{{m}^{2}}\]

Therefore, the area of the square park is \[40,000{{m}^{2}}\].

**Note:**The question should be understood properly as to what is given to us in the form of distance. The formula of the perimeter of a square should be known correctly and the area of a square should be known correctly as well. Also, while substituting the value of the side in the formula of the area of a square, do not forget to square the side or else the obtained area will be incorrect.

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