A rectangle has a length of 64 inches and a width of 32 inches. What is the area, in square...

1. TRANSLATE the problem information

• Given information:
  • Length of rectangle = 64 inches
  • Width of rectangle = 32 inches
  • Need to find: Area in square inches

2. INFER the approach

• Since we need the area of a rectangle and have both dimensions, we should use the rectangle area formula
• The area formula will give us a direct path to the answer

3. Apply the area formula

• Rectangle area formula: \(\mathrm{A = length \times width}\)
• Substitute the known values: \(\mathrm{A = 64 \times 32}\)
• Calculate: \(\mathrm{A = 2048}\)

Answer: 2048 square inches

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Students mix up area and perimeter formulas

Some students remember rectangle formulas but confuse which one to use. They might calculate perimeter instead: \(\mathrm{P = 2(length + width) = 2(64 + 32) = 2(96) = 192}\). This leads to selecting an incorrect answer or confusion when 192 doesn't appear among typical answer choices.

Second Most Common Error:

Weak SIMPLIFY execution: Arithmetic errors in multiplication

Students know the correct formula but make computational mistakes when calculating \(\mathrm{64 \times 32}\). Common errors include getting 1024 (mixing up place values) or other incorrect products. This causes them to select wrong answer choices or abandon their systematic approach.

The Bottom Line:

This problem tests whether students can distinguish between area and perimeter concepts and execute basic multiplication accurately. Success requires both conceptual clarity and computational precision.