A trapezoid has parallel sides with lengths of 18 meters and 26 meters. The height of the trapezoid is 24...

1. TRANSLATE the problem information

• Given information:
  • Parallel sides with lengths: 18 meters and 26 meters
  • Height: 24 meters
  • Need to find: Area in square meters

• What this tells us: We have all the measurements needed for the trapezoid area formula

2. TRANSLATE the geometric formula

• Area formula for trapezoid: \(\mathrm{Area} = \frac{1}{2} \times (\mathrm{sum\,of\,parallel\,sides}) \times \mathrm{height}\)
• Substitute our values: \(\mathrm{Area} = \frac{1}{2} \times (18 + 26) \times 24\)

3. SIMPLIFY through calculation steps

• First, find sum of parallel sides: \(18 + 26 = 44\) meters
• Next, multiply by height: \(44 \times 24 = 1,056\)
• Finally, multiply by 1/2: \(\frac{1}{2} \times 1,056 = 528\)

Answer: A) 528 square meters

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing the 1/2 factor (SIMPLIFY execution error): Students correctly identify the trapezoid formula but forget to include the factor of 1/2 in their calculation.

They calculate: \((18 + 26) \times 24 = 44 \times 24 = 1,056\)

This leads them to select Choice C (1,056) instead of the correct answer.

The Bottom Line:

This problem tests whether students can accurately recall and apply the complete trapezoid area formula. The key challenge is remembering that trapezoid area, like triangle area, includes a factor of 1/2 - it's not just base times height like rectangle area.