A garden plot is shaped like a trapezoid. The two parallel sides of the plot have lengths of 15 feet...

1. INFER the problem type and approach

• This is asking for the area of a trapezoid
• We need to use the trapezoid area formula: \(\mathrm{A = \frac{1}{2}(b_1 + b_2)h}\)
• This formula requires the lengths of both parallel sides (bases) and the height

2. TRANSLATE the given information to match the formula

• Given information:
  • Two parallel sides: 15 feet and 25 feet (these are our bases \(\mathrm{b_1}\) and \(\mathrm{b_2}\))
  • Height: 10 feet (this is our \(\mathrm{h}\))
• So: \(\mathrm{b_1 = 15}\) feet, \(\mathrm{b_2 = 25}\) feet, \(\mathrm{h = 10}\) feet

3. SIMPLIFY by substituting and calculating

• Substitute into the formula: \(\mathrm{A = \frac{1}{2}(15 + 25)(10)}\)
• Add the bases first: \(\mathrm{15 + 25 = 40}\)
• Now we have: \(\mathrm{A = \frac{1}{2}(40)(10)}\)
• Multiply: \(\mathrm{A = \frac{1}{2}(400) = 200}\)

Answer: 200 square feet (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Doesn't remember the trapezoid area formula or confuses it with other area formulas.

Some students might try to use rectangle formula (length × width) or triangle formula (1/2 × base × height), leading to incorrect calculations like \(\mathrm{15 \times 10 = 150}\) or \(\mathrm{25 \times 10 = 250}\). This may lead them to select Choice C (150) if they use rectangle thinking with the smaller base.

Second Most Common Error:

Weak SIMPLIFY execution: Makes arithmetic errors in the multi-step calculation.

Students might incorrectly calculate \(\mathrm{\frac{1}{2}(15 + 25)(10)}\) by not following proper order of operations, perhaps calculating \(\mathrm{\frac{1}{2}(15) + 25 \times 10 = 7.5 + 250 = 257.5}\), or making other arithmetic mistakes. This leads to confusion and guessing among the given choices.

The Bottom Line:

This problem tests whether students recognize the trapezoid area situation and can systematically apply the correct formula with careful arithmetic—two fundamental skills that often get rushed in geometry problems.