What is the area, in square inches, of a rectangle with a length of 7 inches and a width of...

1. TRANSLATE the problem information

• Given information:
  • Rectangle length: 7 inches
  • Rectangle width: 6 inches
  • Need to find: area in square inches

2. INFER the approach needed

• To find area of a rectangle, we need to use the area formula
• Area formula: \(\mathrm{A = length \times width}\)
• We have both dimensions, so we can substitute directly

3. Apply the formula and calculate

• \(\mathrm{A = length \times width}\)
• \(\mathrm{A = 7 \times 6 = 42}\)
• The area is 42 square inches

Answer: C. 42

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misunderstand what "area" means and think it requires adding the dimensions instead of multiplying them.

Instead of recognizing that area measures the space inside a shape (requiring \(\mathrm{length \times width}\)), they treat it like perimeter or just combine the numbers by adding: \(\mathrm{7 + 6 = 13}\).

This leads them to select Choice A (13).

Second Most Common Error:

Conceptual confusion about area: Students may remember that rectangle calculations involve both dimensions but apply an incorrect operation or make calculation errors.

Some students might double their work or misremember a formula step, leading to calculation errors that could result in other incorrect choices like Choice D (84) or getting confused and guessing.

The Bottom Line:

This problem tests the most fundamental geometric calculation - rectangle area. The key challenge is that students must clearly understand that "area" specifically means multiplying the two dimensions, not adding them or applying any other operation.