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Understanding the perimeter calculation is essential in geometry. Perimeter is the total distance around the edge of a polygon, and for regular shapes, like a square, calculating it is quite straightforward. To find the perimeter of a square, one would multiply the length of one of its sides by four, since all sides are equal in length.

For instance, in our specific problem, if the perimeter is given as 48 inches, then dividing this value by 4—since a square has four sides—provides us with the length of one side. The formula applied here is simply: \[ \text{Perimeter of a square} = 4 \times \text{side length} \]. So, inversely we can find the side length by dividing the perimeter by 4: \[ \text{side length} = \frac{\text{Perimeter of a square}}{4} \]. When put into practice for our exercise: \[ \text{side length} = \frac{48\,\text{in}}{4} = 12\,\text{in} \]. This simple division is a fundamental skill in prealgebra that helps in solving many geometric problems.

Squares are very special shapes in geometry. They belong to the family of quadrilaterals and possess several unique properties that make them easy to work with.

Key properties of a square include:

• All four sides are of equal length.
• Every angle in a square is a right angle (90 degrees).
• The diagonals of a square are equal in length and bisect each other at right angles.
• The opposite sides are parallel to each other.

When we look at any problem involving squares, these properties provide us with multiple ways to understand and solve it. In the case of our exercise, knowing that all sides of a square have equal length is crucial because it tells us that once we find the length of one side, we have essentially solved for all four.

In prealgebra, problem-solving skills are developed by understanding how to approach and solve different types of equations and problems. A solid approach often involves the following steps:

Step-by-step problem-solving approach:

• Identify the information given: This involves understanding what the problem provides you, such as the perimeter of the square in the given exercise.
• Create a strategy: Determine the steps you need to take to find a solution. For geometry problems, this might mean recalling relevant formulas and properties of shapes.
• Solve: Apply the formulas and the information given to find the solution. In our example, this involved dividing the total perimeter by 4 to find the length of one side.
• Review: After solving, it's a good habit to revisit the problem to ensure that your answer is reasonable and that all steps have been followed correctly.

By mastering these problem-solving steps in prealgebra, students can build a strong foundation that will be useful in higher levels of mathematics.