A triangular lot has an area of 54 square meters. The base of the triangle measures 9 meters. What is...

1. TRANSLATE the problem information

• Given information:
  • Area of triangle = \(54\) square meters
  • Base of triangle = \(9\) meters
  • Need to find: height of triangle

2. INFER the approach

• We need the triangle area formula to connect area, base, and height
• Since we know area and base, we can solve for height

3. SIMPLIFY using the triangle area formula

• Start with: \(\mathrm{A} = \frac{1}{2}\mathrm{bh}\)
• Substitute known values: \(54 = \frac{1}{2}(9)(\mathrm{h})\)
• Simplify the right side: \(54 = 4.5\mathrm{h}\)
• Divide both sides by 4.5: \(\mathrm{h} = 54 ÷ 4.5 = 12\)

Answer: C. 12

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Forgetting the factor of 1/2 in the triangle area formula

Students may recall the area formula incorrectly as \(\mathrm{A} = \mathrm{bh}\) (confusing it with rectangle area), leading to:

\(54 = 9\mathrm{h} \rightarrow \mathrm{h} = 6\)

This may lead them to select Choice A (6)

Second Most Common Error:

Weak SIMPLIFY execution: Making arithmetic errors in the division step

Students set up the problem correctly but struggle with dividing 54 by 4.5, potentially getting confused with decimal division or making computational mistakes.

This leads to confusion and guessing among the remaining answer choices.

The Bottom Line:

This problem tests whether students can recall the correct triangle area formula and perform accurate decimal division. The key insight is recognizing that triangle area includes the factor of 1/2, unlike rectangular area formulas.