A square has a perimeter of 48 centimeters. What is the area, in square centimeters, of the square?

1. TRANSLATE the problem information

• Given information:
  • Square has perimeter of 48 centimeters
  • Need to find the area in square centimeters

2. INFER the solution strategy

• To find area, we need the side length first
• We can get side length from the perimeter using \(\mathrm{P = 4s}\)

3. TRANSLATE perimeter information into equation

• Perimeter formula: \(\mathrm{P = 4s}\)
• Substitute given value: \(\mathrm{48 = 4s}\)

4. SIMPLIFY to find side length

• Solve for s: \(\mathrm{s = 48 ÷ 4 = 12}\) centimeters

5. TRANSLATE to area calculation

• Area formula: \(\mathrm{A = s^2}\)
• Substitute side length: \(\mathrm{A = 12^2}\)

6. SIMPLIFY to get final area

• Calculate: \(\mathrm{A = 144}\) square centimeters

Answer: B) 144

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may try to directly use the perimeter value (48) in the area formula, thinking area relates directly to perimeter without finding the side length first.

They might calculate something like \(\mathrm{48^2 ÷ 4 = 2304 ÷ 4 = 576}\), reasoning that they need to "adjust" the perimeter somehow to get area.

This may lead them to select Choice D (576).

Second Most Common Error:

Formula confusion: Students may remember that both perimeter and area involve the side length but mix up how to apply the formulas.

They might think area = perimeter × side ÷ 4 or use some other incorrect relationship between the two concepts.

This leads to confusion and guessing among the remaining answer choices.

The Bottom Line:

This problem tests whether students can work systematically through a two-step process: perimeter → side length → area. The key insight is recognizing that the side length is the bridge between these two different measurements of the square.