What is the area, in square centimeters, of a rectangle with a length of 36 centimeters and a width of...

1. TRANSLATE the problem information

• Given information:
  • Length of rectangle = 36 centimeters
  • Width of rectangle = 34 centimeters
  • Need to find: Area in square centimeters

2. INFER the correct approach

• Since we need area (not perimeter), we multiply the dimensions
• Area formula for rectangle: \(\mathrm{A = length \times width}\)
• We have both dimensions, so we can calculate directly

3. Apply the formula and calculate

\(\mathrm{A = 36 \times 34}\)

\(\mathrm{A = 1,224}\) square centimeters

Answer: D. 1,224

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse area with perimeter and add the dimensions instead of multiplying them.

They might think: "I need to do something with 36 and 34... let me add them: \(\mathrm{36 + 34 = 70}\)." Or they might remember that perimeter involves adding but forget to double it, leading to the same result.

This may lead them to select Choice A (70).

Second Most Common Error:

Conceptual confusion about area vs. perimeter: Students remember that perimeter uses addition but apply the full perimeter formula \(\mathrm{P = 2(length + width)}\).

They calculate: \(\mathrm{P = 2(36 + 34) = 2(70) = 140}\), thinking this gives them the area.

This may lead them to select Choice B (140).

The Bottom Line:

This problem tests whether students can distinguish between area (which multiplies dimensions) and perimeter (which adds them). The key insight is recognizing that "area" means we need to multiply length × width, not add the sides together.