Introduction:
In this problem, we are given a square and a rectangular field with the same perimeter. We need to determine which field has a larger area. To solve this problem, we will compare the areas of both shapes and analyze their dimensions.

Analysis:
Let's consider the square field first. Since all sides of a square are equal, let's assume the length of one side as 's'. The perimeter of the square is given by 4s.

Now let's consider the rectangular field. Let's assume the length of the rectangle as 'l' and the width as 'w'. The perimeter of the rectangular field is given by 2(l + w).

Since the two fields have the same perimeter, we can set up the following equation:
4s = 2(l + w)

Simplifying the equation, we get:
2s = l + w

Now let's compare the areas of the square and the rectangle.

Area of the Square:
The area of a square is given by the formula A = s^2, where 's' is the length of one side.
So, the area of the square field is A(square) = s^2.

Area of the Rectangle:
The area of a rectangle is given by the formula A = l * w, where 'l' is the length and 'w' is the width.
So, the area of the rectangular field is A(rectangle) = l * w.

Comparison:
To determine which field has a larger area, we need to compare A(square) and A(rectangle).

Substituting 2s = l + w into the equation A(rectangle) = l * w, we get:
A(rectangle) = (2s - w) * w

To find the maximum area, we can differentiate A(rectangle) with respect to 'w' and equate it to zero. However, since we are not given any specific values for 's' or 'w', we cannot find the exact maximum area.

Conclusion:
In conclusion, based on the given information, we cannot determine which field has a larger area. The areas of the square and the rectangle depend on the specific values of 's' and 'w'.