What is the area of a rectangle with a length of 4 cm and a width of 2 cm?

1. TRANSLATE the problem information

• Given information:
  • Rectangle length = 4 cm
  • Rectangle width = 2 cm
• What we need to find: Area of the rectangle

2. INFER the appropriate formula

• For area of a rectangle, we multiply length times width
• Formula: \(\mathrm{Area = length \times width}\)
• This is different from perimeter, which adds the sides

3. SIMPLIFY by substituting and calculating

• \(\mathrm{Area = 4\,cm \times 2\,cm}\)
• \(\mathrm{Area = 8\,cm^2}\)
• Note: The units become cm² because we're multiplying two length measurements

Answer: B. 8 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 need to do something with 4 and 2... maybe add them?" This gives them \(\mathrm{4 + 2 = 6}\).

This may lead them to select Choice A (6 cm²)

Second Most Common Error:

Weak INFER skill: Students remember that perimeter involves adding sides but apply the full perimeter formula when asked for area.

They calculate:

\(\mathrm{Perimeter = 2(length + width)}\)

\(\mathrm{= 2(4 + 2)}\)

\(\mathrm{= 2(6)}\)

\(\mathrm{= 12}\)

thinking this might be the area.

This may lead them to select Choice C (12 cm²)

The Bottom Line:

The key challenge is distinguishing between area (which involves multiplication) and perimeter (which involves addition). Students must recognize that "area" specifically requires multiplying the dimensions, not adding them in any form.