A triangle has a base length of 40 centimeters and a height of 90 centimeters. What is the area, in...

1. TRANSLATE the problem information

• Given information:
  • Base length = 40 centimeters
  • Height = 90 centimeters
  • Need to find: Area in square centimeters

2. INFER the approach

• We need the triangle area formula to connect base and height to area
• The formula A = (1/2) × base × height applies to any triangle when we know base and height

3. SIMPLIFY the calculation

\(\mathrm{A = \frac{1}{2} \times base \times height}\)

\(\mathrm{A = \frac{1}{2} \times 40 \times 90}\)

\(\mathrm{A = \frac{1}{2} \times 3600}\)

\(\mathrm{A = 1800}\)

Answer: 1800

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about the triangle area formula: Students remember that area involves base and height but forget the crucial 1/2 factor

They calculate: \(\mathrm{A = base \times height = 40 \times 90 = 3600}\)

This leads them to an answer of 3600 instead of the correct 1800.

Second Most Common Error:

Weak SIMPLIFY execution: Students know the correct formula but make arithmetic mistakes in the multi-step calculation

For example, they might incorrectly calculate (1/2) × 3600 or make errors when multiplying 40 × 90, leading to various incorrect numerical answers.

The Bottom Line:

This problem tests whether students can recall and correctly apply the triangle area formula. The key insight is remembering that triangle area is exactly half the area of a rectangle with the same base and height - hence the 1/2 factor is essential.