A triangle has a base of 40 inches and a height of 30 inches. What is the area, in square...

1. TRANSLATE the problem information

• Given information:
  • Base = 40 inches
  • Height = 30 inches
• What we need to find: Area of the triangle in square inches

2. INFER the approach

• Since we have base and height of a triangle, we should use the triangle area formula
• The formula is: \(\mathrm{Area} = \frac{1}{2} \times \mathrm{base} \times \mathrm{height}\)

3. SIMPLIFY by substituting values and calculating

• \(\mathrm{Area} = \frac{1}{2} \times 40 \times 30\)
• \(\mathrm{Area} = \frac{1}{2} \times 1,200\)
• \(\mathrm{Area} = 600\) square inches

Answer: 600

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about triangle area formula: Students might forget the "½" factor and use \(\mathrm{Area} = \mathrm{base} \times \mathrm{height}\) (which is the rectangle formula instead of triangle formula).

Using \(\mathrm{Area} = 40 \times 30 = 1,200\), they would get 1,200 square inches instead of the correct 600. This leads to selecting an answer that's exactly double the correct value.

Second Most Common Error:

Weak SIMPLIFY execution: Students might make arithmetic errors when calculating \(\frac{1}{2} \times 40 \times 30\), such as:

• Incorrectly calculating \(40 \times 30 = 1,200\)
• Making errors when dividing 1,200 by 2
• Confusing the order of operations

This leads to various incorrect numerical answers and causes confusion about which choice to select.

The Bottom Line:

This problem tests whether students remember the triangle area formula correctly (especially the ½ factor) and can perform basic arithmetic accurately. The most critical point is distinguishing triangle area from rectangle area formulas.