What is the area of a triangle with a base of 5text{ cm} and a height of 48text{ cm}?60text{ cm}^2100text{...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{Base = 5\ cm}\)
  • \(\mathrm{Height = 48\ cm}\)
  • Asked to find the area

2. Apply the triangle area formula

• Recall: \(\mathrm{Area = \frac{1}{2} \times base \times height}\)
• This formula works for any triangle when you have a perpendicular height

3. SIMPLIFY by substituting and calculating

• Substitute the values: \(\mathrm{Area = \frac{1}{2} \times 5 \times 48}\)
• First multiply: \(\mathrm{5 \times 48 = 240}\)
• Then apply the half: \(\mathrm{240 \div 2 = 120}\)
• Include units: \(\mathrm{120\ cm^2}\)

Answer: \(\mathrm{C\ (120\ cm^2)}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students forget to multiply by \(\mathrm{\frac{1}{2}}\) in the triangle area formula.

They correctly identify the formula and substitute values, but calculate: \(\mathrm{Area = 5 \times 48 = 240\ cm^2}\). They skip the crucial step of dividing by 2 (or multiplying by \(\mathrm{\frac{1}{2}}\)), treating the triangle area formula like it's base × height instead of \(\mathrm{\frac{1}{2} \times base \times height}\).

This leads them to select Choice \(\mathrm{D\ (240\ cm^2)}\).

The Bottom Line:

Triangle area problems are straightforward once you remember the complete formula, but the \(\mathrm{\frac{1}{2}}\) factor is the most commonly forgotten component. The key is systematic execution of all parts of the formula, not just the base × height portion.