The side length of a square is 55 centimeters (cm). What is the area, in cm^2, of the square?

1. TRANSLATE the problem information

• Given information:
  • Square has side length \(\mathrm{s = 55\ cm}\)
  • Need to find area in \(\mathrm{cm^2}\)

2. INFER the correct approach

• For area problems involving squares, use the area formula \(\mathrm{A = s^2}\)
• This is different from perimeter (which would be \(\mathrm{4s}\)) or other measurements

3. SIMPLIFY by applying the formula

• Substitute the side length: \(\mathrm{A = 55^2}\)
• Calculate: \(\mathrm{55^2 = 55 \times 55 = 3,025}\)
• Include units: \(\mathrm{A = 3,025\ cm^2}\)

Answer: C. 3,025

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about area vs. perimeter: Students mix up the formulas and calculate perimeter instead of area.

They might think: "The side is 55, so I need to add all sides: \(\mathrm{55 + 55 + 55 + 55 = 220}\)" or "Maybe it's just \(\mathrm{2 \times 55 = 110}\)."

This may lead them to select Choice B (220) for perimeter, or Choice A (110) for half the perimeter.

Second Most Common Error:

Weak SIMPLIFY execution: Students know to use \(\mathrm{A = s^2}\) but make calculation errors when computing \(\mathrm{55^2}\).

They might miscalculate \(\mathrm{55 \times 55}\), potentially getting values like 12,100 through digit placement errors or incorrect multiplication.

This may lead them to select Choice D (12,100).

The Bottom Line:

Success on this problem requires clearly distinguishing between area (\(\mathrm{s^2}\)) and perimeter (\(\mathrm{4s}\)) formulas, then executing the squaring calculation accurately.