The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface...

1. TRANSLATE the problem information

• Given information:
  • Right rectangular prism with dimensions 4 inches by 5 inches by 6 inches
  • Need to find surface area in square inches

2. INFER the structure and approach

• A right rectangular prism has 6 faces total
• These faces form 3 pairs of congruent rectangles:
  • Two faces with dimensions \(\mathrm{4 \times 5}\)
  • Two faces with dimensions \(\mathrm{5 \times 6}\)
  • Two faces with dimensions \(\mathrm{4 \times 6}\)
• Surface area = sum of areas of all 6 faces

3. SIMPLIFY by calculating each pair of face areas

• Two \(\mathrm{4 \times 5}\) faces: \(\mathrm{2(4 \times 5) = 2(20) = 40}\) square inches
• Two \(\mathrm{5 \times 6}\) faces: \(\mathrm{2(5 \times 6) = 2(30) = 60}\) square inches
• Two \(\mathrm{4 \times 6}\) faces: \(\mathrm{2(4 \times 6) = 2(24) = 48}\) square inches

4. SIMPLIFY to find total surface area

• Surface area = \(\mathrm{40 + 60 + 48 = 148}\) square inches

Answer: D. 148

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students calculate the area of only three faces (one from each pair) instead of recognizing they need all six faces.

They might calculate: \(\mathrm{4 \times 5 + 5 \times 6 + 4 \times 6 = 20 + 30 + 24 = 74}\)

This leads them to select Choice B (74)

Second Most Common Error:

Conceptual confusion about surface area vs. volume: Students mix up the formulas and calculate volume instead.

They multiply all three dimensions: \(\mathrm{4 \times 5 \times 6 = 120}\)

This leads them to select Choice C (120)

The Bottom Line:

This problem tests whether students truly understand what "surface area" means - you need the total area of ALL faces, not just some of them. The key insight is recognizing that opposite faces of a rectangular prism are congruent, so you can calculate efficiently by doubling each unique face area.