What is the area, in square centimeters, of a rectangle with a length of 34 centimeters (cm) and a width...

1. TRANSLATE the problem information

• Given information:
  • Rectangle with \(\mathrm{length = 34\text{ cm}}\)
  • Rectangle with \(\mathrm{width = 29\text{ cm}}\)
  • Need to find: area in square centimeters

2. INFER the appropriate approach

• The problem asks for area, so we need the rectangle area formula
• Area formula: \(\mathrm{A = length \times width}\)
• This means: \(\mathrm{A = 34 \times 29}\)

3. SIMPLIFY the calculation

• \(\mathrm{A = 34 \times 29}\)
• \(\mathrm{A = 986}\)

Answer: 986 (or 986 square centimeters)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Students mix up area and perimeter formulas

Instead of using \(\mathrm{A = length \times width}\), they use the perimeter formula:

\(\mathrm{P = 2(length + width)}\)

\(\mathrm{P = 2(34 + 29)}\)

\(\mathrm{P = 2(63)}\)

\(\mathrm{P = 126}\)

This leads to an answer that's far too small and doesn't match the expected area units.

Second Most Common Error:

Weak SIMPLIFY execution: Students make arithmetic errors when computing \(\mathrm{34 \times 29}\)

Common calculation mistakes include getting 966, 976, or other values close to but not equal to 986. These errors typically come from mistakes in carrying or place value during multiplication.

The Bottom Line:

This is a straightforward application problem that tests whether students can identify the right formula and execute basic multiplication accurately. The key insight is recognizing that "area" means using \(\mathrm{A = \ell w}\), not the perimeter formula.