What is the area, in square centimeters, of a triangle with a base of 12 centimeters and a height of...

1. TRANSLATE the problem information

• Given information:
  • Base = 12 centimeters
  • Height = 8 centimeters
  • Need to find: Area in square centimeters

• This is asking for the area of a triangle when we know the base and height

2. TRANSLATE the approach using the triangle area formula

• Triangle area formula: \(\mathrm{Area} = \frac{1}{2} \times \mathrm{base} \times \mathrm{height}\)
• The key insight: Triangle area is exactly half the area of a rectangle with the same base and height
• Don't forget that crucial \(\frac{1}{2}\) factor!

3. SIMPLIFY by substituting and calculating

• \(\mathrm{Area} = \frac{1}{2} \times 12 \times 8\)
• First multiply the base and height: \(12 \times 8 = 96\)
• Then multiply by \(\frac{1}{2}\): \(\frac{1}{2} \times 96 = 48\)

Answer: C (48)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Forgetting the \(\frac{1}{2}\) factor in the triangle area formula

Students remember they need to multiply base times height, but forget that triangle area is half of a rectangle's area. They calculate: \(12 \times 8 = 96\) square centimeters.

This may lead them to select Choice D (96)

The Bottom Line:

The triangle area formula has that critical \(\frac{1}{2}\) factor because a triangle is exactly half of a rectangle with the same base and height. Students who miss this foundational concept will consistently get triangle area problems wrong.