A triangular prism has a height of 8 centimeters (cm) and a volume of 216 cm³. What is the area,...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{Volume = 216\text{ cm}^3}\)
  • \(\mathrm{Height = 8\text{ cm}}\)
  • Volume formula: \(\mathrm{V = Bh}\)
• What we need to find: Base area (B)

2. INFER the solution approach

• We have the volume formula \(\mathrm{V = Bh}\) and know V and h
• Strategy: Substitute the known values and solve for B
• This is a direct substitution problem

3. SIMPLIFY by substituting and solving

• Start with: \(\mathrm{V = Bh}\)
• Substitute known values: \(\mathrm{216 = B \times 8}\)
• Divide both sides by 8: \(\mathrm{B = 216 \div 8 = 27}\)

Answer: \(\mathrm{27\text{ cm}^2}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students may confuse which variable they're solving for or misidentify what information is given. Some students might think they need to find the height instead of base area, or confuse the volume formula with surface area formulas.

This leads to confusion and abandoning the systematic approach, resulting in guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when dividing 216 by 8, such as getting 26 or 28 instead of 27. This often happens when students rush through the division or don't double-check their calculation.

This may lead them to select an incorrect numerical answer if given multiple choice options.

The Bottom Line:

This problem tests whether students can recognize a direct algebraic substitution situation and execute basic division accurately. The key insight is seeing that when you have \(\mathrm{V = Bh}\) with two of the three variables known, you simply substitute and solve.