The length of each side of a square is 94 centimeters (cm). Which expression gives the area, in cm^2, of...

1. TRANSLATE the problem information

• Given information:
  • Square with side length = \(\mathrm{94\,cm}\)
  • Need to find: expression for area in \(\mathrm{cm^2}\)

2. INFER the appropriate formula

• For any square, \(\mathrm{Area = (side\,length)^2}\)
• Since our side length is \(\mathrm{94\,cm}\): \(\mathrm{Area = 94^2}\)

3. TRANSLATE the mathematical expression to match answer choices

• \(\mathrm{94^2}\) means "94 times 94"
• This can be written as: \(\mathrm{94 \cdot 94}\)
• Looking at the choices, this matches choice D

Answer: D. \(\mathrm{94 \cdot 94}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion between area and perimeter: Students mix up the formulas for area and perimeter of a square.

They remember that squares involve multiplying the side length by something, but incorrectly recall that \(\mathrm{area = 4 \times side}\) (which is actually the perimeter formula). This leads them to think the area is \(\mathrm{4 \times 94}\).

This may lead them to select Choice C (\(\mathrm{4 \cdot 94}\)).

Second Most Common Error:

Weak TRANSLATE skill: Students correctly know that \(\mathrm{area = side^2}\), but don't recognize that "\(\mathrm{94^2}\)" is the same as "\(\mathrm{94 \cdot 94}\)" when looking at the answer choices.

They might see \(\mathrm{94^2}\) and look for an expression that literally shows an exponent, not realizing that multiplication is equivalent. This causes confusion about which choice represents their calculated answer.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can distinguish between area and perimeter formulas for squares, and whether they can recognize that \(\mathrm{s^2}\) and \(\mathrm{s \cdot s}\) represent the same mathematical operation.