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Understanding geometry principles is key to solving a multitude of problems related to shapes, sizes, and properties of space. Specifically, in the context of finding the perimeter of a square, it's crucial to first identify the characteristics of a square—including the fact that all four sides are of equal length, and each of the angles is a right angle. When these principles are not clear, there can be confusion, as in the case of the exercise where both sides RI and IS are given different measurements. This suggests a need for further clarification since the definition of a square does not allow for adjacent sides to differ in length. It could be a case of mistaken identity where the figure might actually be a rectangle instead of a square.

When tackling problems in geometry, one of the first steps should always be to verify the properties of the shape being discussed and ensure that all given information aligns with those properties. This is an important part of the problem-solving process as it lays the foundation for the correct application of geometrical formulas and principles.

Calculating the perimeter of a shape involves adding up the lengths of all the sides that outline the shape. For polygons with equal side lengths, such as a square, this process is even more straightforward. The perimeter is simply the length of one side multiplied by the total number of sides. In the case of a square, there are four sides, and thus, the formula to calculate the perimeter (P) is expressed as: \[ P = 4 \times \text{side length} \]

However, as noted in the exercise improvement advice, without a clear confirmation that the figure is indeed a square, simply assuming a side length and applying this formula can lead to errors. It's vital to ensure that the shape complies with geometric principles before proceeding with calculations. This avoidance of premature calculation not only applies to squares but is a good practice when dealing with any geometrical problem.

Squares hold a unique place in geometry due to their distinct properties. Each of a square's four sides is of the same length, and the internal angles are all right angles, being 90 degrees each. Also, the opposing sides are parallel, and the diagonals are equal in length and bisect each other at right angles. These properties make squares highly symmetrical, which simplifies calculations related to area and perimeter.

In the exercise provided, identifying the properties of the square is where the difficulty lies. A square cannot have two adjacent sides of different lengths, reinforcing the likelihood of a misconception: either the shape is not a square, or the given measurements are incorrect. If all sides of the square were confirmed to be 17 units or 13 units, only then would the calculation of the perimeter be straightforward and in line with the defining properties of a square.