The length of each edge of a box is 29 inches. Each side of the box is in the shape...

1. TRANSLATE the problem information

• Given information:
  • Edge length: 29 inches
  • Each side is square-shaped
  • Box has no lid
  • Need exterior surface area

• What this tells us: We have a cube-shaped container missing its top face

2. INFER how many faces to count

• A complete cube has 6 square faces
• Since there's no lid, we have: 1 bottom + 4 sides = 5 faces total
• All faces are congruent squares with 29-inch sides

3. Calculate area of one square face

• Area of square = \(\mathrm{side}^2\)
• Area = \(29^2 = 841\) square inches

4. INFER the total surface area approach

• Surface area = sum of all face areas
• Since all 5 faces are identical: Total = \(5 \times \mathrm{(area\ of\ one\ face)}\)
• Total surface area = \(5 \times 841 = 4,205\) square inches

Answer: 4205

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret 'box without a lid' and count 6 faces instead of 5

Many students automatically think 'cube = 6 faces' without carefully reading that the box has no lid. They calculate \(6 \times 841 = 5,046\), leading to an incorrect answer that's too large.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students make arithmetic errors when calculating \(29^2\) or the final multiplication

Some students might miscalculate \(29^2\) (perhaps getting 829 instead of 841) or make errors in \(5 \times 841\), leading to various incorrect values.

The Bottom Line:

This problem tests careful reading comprehension combined with 3D spatial reasoning. Students must visualize that removing the lid from a cube leaves exactly 5 faces, then execute straightforward area calculations accurately.