A triangle has a base length of 10 centimeters and a corresponding height of 70 centimeters. What is the area,...

1. TRANSLATE the problem information

• Given information:
  • Base length: 10 centimeters
  • Corresponding height: 70 centimeters
  • Need to find: Area in square centimeters

2. INFER the approach

• Since we need to find the area of a triangle and we have the base and height, we need the triangle area formula
• Triangle area formula: \(\mathrm{A = \frac{1}{2}bh}\)
• We have all the values needed: \(\mathrm{b = 10}\) and \(\mathrm{h = 70}\)

3. SIMPLIFY by substituting and calculating

• \(\mathrm{A = \frac{1}{2}bh}\)
• \(\mathrm{A = \frac{1}{2}(10)(70)}\)
• \(\mathrm{A = \frac{1}{2}(700)}\)
• \(\mathrm{A = 350}\)

Answer: B. 350

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Forgetting the 1/2 factor in the triangle area formula

Students remember that area involves base times height but forget that triangles require the 1/2 factor (unlike rectangles where Area = length × width). They calculate: \(\mathrm{Area = base \times height = 10 \times 70 = 700}\).

This may lead them to select Choice A (700).

Second Most Common Error:

Conceptual confusion: Mixing up area calculation with simple addition

Some students, when unsure about formulas, resort to combining the given numbers in the simplest way possible. They calculate: \(\mathrm{10 + 70 = 80}\), thinking this might give them the area.

This may lead them to select Choice D (80).

The Bottom Line:

This problem tests whether students can recall and correctly apply the triangle area formula. The given values are straightforward, but success depends entirely on remembering that triangle area requires the 1/2 factor, unlike rectangular area.