What is the area of a rectangle with a length of 17 centimeters (cm) and a width of 7 cm?

1. TRANSLATE the problem information

• Given information:
  • Rectangle length: 17 cm
  • Rectangle width: 7 cm
  • Need to find: area

2. INFER the approach

• For rectangles, area is found by multiplying length times width
• We have both measurements, so we can apply: \(\mathrm{A = length \times width}\)

3. Apply the formula

• \(\mathrm{A = 17\ cm \times 7\ cm = 119\ cm^2}\)
• The units become cm² because we're multiplying cm × cm

Answer: C. 119 cm²

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse area with perimeter and add the dimensions instead of multiplying them.

They think: "I have two measurements of a rectangle, so I add them: \(\mathrm{17 + 7 = 24}\)"

This may lead them to select Choice A (24 cm²)

Second Most Common Error:

Weak INFER skill: Students remember that perimeter involves adding dimensions but apply the full perimeter formula \(\mathrm{P = 2(l + w)}\).

They calculate: "\(\mathrm{2(17 + 7) = 2(24) = 48}\)"

This may lead them to select Choice B (48 cm²)

The Bottom Line:

Rectangle problems require distinguishing between area (multiply dimensions) and perimeter (add dimensions, then double). The key insight is recognizing that "area" always means multiplying the dimensions together.