A regular pentagon has a side length of 7 inches. What is the perimeter, in inches, of the pentagon?

1. TRANSLATE the problem information

• Given information:
  • Shape: regular pentagon
  • Side length: 7 inches
  • Find: perimeter in inches

• What this tells us: We have a 5-sided shape where all sides are the same length.

2. INFER the solution strategy

• Since all sides of a regular pentagon are equal, we can find the total perimeter by multiplying one side length by the total number of sides.
• Strategy: Find (number of sides) × (length of one side)

3. Apply the perimeter calculation

• Number of sides in a pentagon: 5
• Perimeter = \(5 \times 7 = 35\) inches

Answer: B (35)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about polygon names: Students may confuse a pentagon with other polygons and use the wrong number of sides.

For example, if they think a pentagon has 4 sides (confusing with square), they calculate \(4 \times 7 = 28\) and select Choice A (28). If they think it has 6 sides (confusing with hexagon), they calculate \(6 \times 7 = 42\) and select Choice C (42).

Second Most Common Error:

Weak INFER reasoning about perimeter calculation: Students may incorrectly think they need to multiply the side length by itself rather than by the number of sides.

This leads them to calculate \(7 \times 7 = 49\) and select Choice D (49).

The Bottom Line:

This problem tests whether students can accurately recall basic polygon definitions and apply the straightforward perimeter formula for regular polygons. The key is knowing that "pentagon" specifically means 5 sides.