A triangular banner has a base of 28 feet and a height of 27 feet. What is the area of...

1. TRANSLATE the problem information

• Given information:
  • Base of triangular banner = 28 feet
  • Height of triangular banner = 27 feet
  • Need to find: Area in square feet

2. INFER the approach

• This is asking for the area of a triangle
• I need to use the triangle area formula: \(\mathrm{A = \frac{1}{2} \times base \times height}\)
• I have both the base and height values needed

3. SIMPLIFY by substituting and calculating

• \(\mathrm{A = \frac{1}{2} \times base \times height}\)
• \(\mathrm{A = \frac{1}{2} \times 28 \times 27}\)
• \(\mathrm{A = 14 \times 27}\)
• \(\mathrm{A = 378}\) square feet

Answer: C (378)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Students don't remember or confuse the triangle area formula

Some students might use \(\mathrm{A = base \times height}\) (forgetting the \(\mathrm{\frac{1}{2}}\) factor), leading them to calculate \(\mathrm{28 \times 27 = 756}\). This may lead them to select Choice D (756).

Second Most Common Error:

Weak SIMPLIFY execution: Arithmetic mistakes in multiplication

Students might make calculation errors when computing \(\mathrm{14 \times 27}\), possibly getting 280 instead of 378. This may lead them to select Choice B (280).

The Bottom Line:

This problem tests whether students can recall and correctly apply the triangle area formula. The most critical step is remembering to include the factor of \(\mathrm{\frac{1}{2}}\), which distinguishes triangles from rectangles and parallelograms.