A trapezoid has parallel sides of lengths 18 centimeters and 26 centimeters. The height of the trapezoid is 12 centimeters....

1. INFER what type of problem this is

• This is asking for the area of a trapezoid
• I need to use the trapezoid area formula since I have the measurements of parallel sides and height

2. TRANSLATE the given information into formula variables

• Given information:
  • Parallel sides: 18 cm and 26 cm (these are \(\mathrm{b_1}\) and \(\mathrm{b_2}\))
  • Height: 12 cm (this is \(\mathrm{h}\))
• The trapezoid area formula is: \(\mathrm{Area} = \frac{1}{2}(\mathrm{b_1} + \mathrm{b_2})\mathrm{h}\)

3. SIMPLIFY by substituting and calculating

• Substitute the values:
  \(\mathrm{Area} = \frac{1}{2}(18 + 26)(12)\)
• Add the parallel sides first:
  \(\mathrm{Area} = \frac{1}{2}(44)(12)\)
• Multiply \(\frac{1}{2} \times 44 = 22\):
  \(\mathrm{Area} = 22 \times 12\)
• Final calculation:
  \(\mathrm{Area} = 264\) square centimeters

Answer: 264

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize this as a trapezoid area problem and instead use a simpler formula like rectangle area (length × width). They might multiply \(18 \times 12 = 216\) or \(26 \times 12 = 312\), thinking of the trapezoid as a rectangle.

This leads to confusion when their answer doesn't match any reasonable expectation for the problem.

Second Most Common Error:

Poor SIMPLIFY execution: Students know to use the trapezoid formula but forget the \(\frac{1}{2}\) factor. They calculate \((18 + 26) \times 12 = 44 \times 12 = 528\), getting exactly double the correct answer.

This leads to an incorrect final answer of 528 square centimeters.

The Bottom Line:

This problem requires students to distinguish trapezoids from other quadrilaterals and remember that the trapezoid area formula includes a \(\frac{1}{2}\) factor - it's not just adding the bases and multiplying by height.