The base of a right prism is a right triangle with legs of lengths 6 units and 8 units. The...

1. TRANSLATE the problem information

• Given information:
  • Base is a right triangle with legs 6 units and 8 units
  • Volume of prism is 2,880 cubic units
  • Need to find the height of the prism

2. INFER the solution approach

• To find the height using V = Base Area × Height, we first need the base area
• Since the base is a right triangle, we can calculate its area using the legs

3. Calculate the base area

• Area of right triangle = \(\frac{1}{2} \times \mathrm{leg_1} \times \mathrm{leg_2}\)
• Area = \(\frac{1}{2} \times 6 \times 8 = 24\) square units

4. SIMPLIFY to find the height

• Using Volume = Base Area × Height:
• \(2{,}880 = 24 \times \mathrm{h}\)
• \(\mathrm{h} = 2{,}880 \div 24 = 120\) units

Answer: C (120)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about triangle measurements: Students may confuse the triangle's legs (6 and 8) with the base and height of the entire prism, trying to use 6 or 8 as the prism height directly.

They might calculate: \(\mathrm{Volume} \div 6 = 2{,}880 \div 6 = 480\) or \(\mathrm{Volume} \div 8 = 2{,}880 \div 8 = 360\), leading to confusion since neither appears in the answer choices. This leads to guessing.

Second Most Common Error:

Missing the triangle area formula: Students may forget to use \(\frac{1}{2}\) in the right triangle area calculation, computing base area as \(6 \times 8 = 48\) instead of 24.

This gives them \(\mathrm{h} = 2{,}880 \div 48 = 60\), leading them to select Choice A (60).

The Bottom Line:

This problem requires clear understanding that the 'base' of the prism is the triangular face, and its area must be calculated before using the volume formula.