A rhombus has diagonals with lengths of 16 centimeters and 24 centimeters. What is the area, in square centimeters, of...

1. TRANSLATE the problem information

• Given information:
  • Rhombus has diagonals with lengths 16 cm and 24 cm
  • Need to find the area

2. INFER the appropriate formula

• For a rhombus, when given diagonal lengths, use: \(\mathrm{Area} = \frac{1}{2} \times \mathrm{d_1} \times \mathrm{d_2}\)
• This is the most direct approach since we have both diagonal measurements

3. SIMPLIFY the calculation

• Substitute the values: \(\mathrm{Area} = \frac{1}{2} \times 16 \times 24\)
• Calculate step by step: \(16 \times 24 = 384\)
• Then: \(\mathrm{Area} = \frac{1}{2} \times 384 = 192\) square centimeters

Answer: (B) 192

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students attempt to use the wrong area formula, such as \(\mathrm{base} \times \mathrm{height}\), because they don't recognize that diagonal lengths require the specific diagonal formula.

Without the diagonal formula, students might try to find side lengths or heights that aren't given, leading to confusion and abandoning systematic solution. This leads to guessing among the answer choices.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students use the correct formula but forget the (1/2) factor, calculating \(\mathrm{Area} = 16 \times 24 = 384\) directly.

This computational oversight leads them to select Choice (D) (384) instead of the correct answer.

The Bottom Line:

This problem tests whether students can match the given information (diagonal lengths) to the appropriate formula. The key insight is recognizing that rhombus area problems with diagonal measurements require the specific diagonal formula, not the general base × height approach.