The base of a right triangular prism is a right triangle with legs of length 8 units and 15 units....

1. TRANSLATE the problem information

• Given information:
  • Right triangular prism with base triangle having legs 8 units and 15 units
  • Total volume = 1,800 cubic units
  • Need to find: height of the prism

2. INFER the solution strategy

• To find prism height using volume, we need the base area first
• Strategy: Calculate base area → Use volume formula → Solve for height

3. Calculate the triangular base area

• For a right triangle: \(\mathrm{Area} = \frac{1}{2} \times \mathrm{leg_1} \times \mathrm{leg_2}\)
• Base area = \(\frac{1}{2} \times 8 \times 15 = 60\) square units

4. SIMPLIFY using the volume formula

• \(\mathrm{Volume} = \mathrm{Base\ area} \times \mathrm{Height}\)
• \(1,800 = 60 \times \mathrm{Height}\)
• \(\mathrm{Height} = 1,800 \div 60 = 30\) units

Answer: B. 30

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students see the calculated base area of 60 and mistakenly think this IS the height they're looking for, without recognizing they need to continue with the volume formula.

This leads them to select Choice (C) (60).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse the base triangle dimensions with the prism height, thinking one of the triangle's legs (8 or 15) must be the prism height.

This may lead them to select Choice (A) (15).

The Bottom Line:

This problem requires clear strategic thinking - students must recognize that finding the prism height is a two-step process requiring the base area as an intermediate step, not the final answer.