A rectangular prism storage container is designed with an open top (no lid). The container has a length of 24...

1. TRANSLATE the problem information

• Given information:
  • Rectangular prism storage container
  • Open top (no lid)
  • Length = \(24\text{ cm}\), Width = \(18\text{ cm}\), Height = \(12\text{ cm}\)
  • Find total surface area of material needed

• What this tells us: We need to calculate the area of all exterior faces except the top face.

2. INFER which faces to calculate

• Since the container has an open top, we have exactly 5 faces:
  • 1 bottom face (rectangle)
  • 4 side faces (2 pairs of identical rectangles)

• Strategy: Calculate each type of face, then add them all together.

3. SIMPLIFY by calculating each face area

• Bottom face area: \(24 \times 18 = 432\text{ cm}^2\)

• Long side faces (there are 2 of them):
  • Each long side: \(24 \times 12 = 288\text{ cm}^2\)
  • Both long sides: \(2 \times 288 = 576\text{ cm}^2\)

• Short side faces (there are 2 of them):
  • Each short side: \(18 \times 12 = 216\text{ cm}^2\)
  • Both short sides: \(2 \times 216 = 432\text{ cm}^2\)

4. SIMPLIFY the final calculation

• Total surface area: \(432 + 576 + 432 = 1440\text{ cm}^2\)

Answer: 1440

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students miss the significance of "open top" and calculate all 6 faces of a complete rectangular prism.

They calculate: Bottom + Top + 4 sides = \(432 + 432 + 576 + 432 = 1872\text{ cm}^2\)

This leads to confusion when their answer doesn't match any reasonable expectation.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify the 5 faces but make arithmetic errors in calculating face areas or adding them up.

For example, they might calculate \(18 \times 12 = 226\) instead of \(216\), leading to an incorrect final sum.

This causes computational errors that result in answers close to but not exactly 1440.

The Bottom Line:

This problem tests whether students can translate a real-world constraint (open container) into mathematical terms (5 faces instead of 6) and then execute systematic area calculations without computational errors.