A right rectangular prism has a length of \(28\text{ centimeters (cm)}\), a width of 15text{ cm}, and a height of...

1. TRANSLATE the problem information

• Given information:
  • Length = 28 cm
  • Width = 15 cm
  • Height = 16 cm
  • Need to find: surface area in cm²

• Surface area means the total area of all the outer faces of the 3D shape

2. INFER the structure of a rectangular prism

• A rectangular prism (box shape) has exactly 6 rectangular faces
• Opposite faces are identical, so we have 3 pairs of congruent faces:
  • 2 faces with dimensions \(\mathrm{length \times width}\)
  • 2 faces with dimensions \(\mathrm{length \times height}\)
  • 2 faces with dimensions \(\mathrm{width \times height}\)

3. SIMPLIFY by calculating each pair of face areas

• Front and back faces: \(\mathrm{2 \times (28 \times 15) = 2 \times 420 = 840\text{ cm}^2}\)
• Left and right faces: \(\mathrm{2 \times (28 \times 16) = 2 \times 448 = 896\text{ cm}^2}\)
• Top and bottom faces: \(\mathrm{2 \times (15 \times 16) = 2 \times 240 = 480\text{ cm}^2}\)

4. SIMPLIFY to find total surface area

• Total surface area = \(\mathrm{840 + 896 + 480 = 2216\text{ cm}^2}\)

Answer: 2216 cm²

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that they need to account for ALL six faces of the prism. They might calculate the area of only three faces (\(\mathrm{28\times 15}\), \(\mathrm{28\times 16}\), \(\mathrm{15\times 16}\)) and get \(\mathrm{420 + 448 + 240 = 1108}\), forgetting that each face appears twice. This leads to selecting an answer that's exactly half the correct value.

Second Most Common Error:

Conceptual confusion: Students mix up surface area with volume and attempt to calculate \(\mathrm{28 \times 15 \times 16 = 6720}\), leading to confusion when this doesn't match any reasonable answer choice. This causes them to abandon systematic solution and guess.

The Bottom Line:

This problem tests whether students truly understand that surface area means "painting all the outside surfaces" - you need the area of every single face, not just one of each type. The key insight is recognizing the 3D structure and that opposite faces are identical.