Questions: Area of Rectangles

Question 1

A rectangle is 8 cm long and 5 cm wide. Which of the following correctly states its area?

• A. 13 cm
• B. 26 cm
• C. 40 cm
• D. 40 cm²

Answer: (D)

Area = length × width = 8 × 5 = 40. The result must be in square centimeters (cm²), not centimeters — area measures surface, not length, so its unit is always a square unit. Option A (13 cm) adds the dimensions instead of multiplying, which finds neither area nor perimeter correctly. Option B (26 cm) finds the perimeter (2 × 8 + 2 × 5), a different measurement entirely. Option C (40 cm) gets the number right but uses the wrong unit.

Question 2

Area and perimeter both measure the same property of a rectangle — they just use different formulas.

• T. True
• F. False

Answer: False

Area and perimeter measure completely different things. Perimeter is the total length of the boundary — it is measured in linear units (cm, m, etc.) and tells you how far you would walk around the rectangle. Area is the amount of surface the rectangle covers — measured in square units (cm², m²) and tells you how many unit squares fit inside. Two rectangles can have the same perimeter but very different areas, and vice versa.

Question 3

Explain in your own words why the area formula for a rectangle is length × width and not length + width.

Model answer: If you tile a rectangle with unit squares, the number of squares in each row equals the width, and the number of rows equals the length. The total count of squares is the number of rows times the number per row — length times width. Addition would only give the number of squares along two sides, not the full interior.

Multiplication counts the total entries in a rectangular array — this is the core model for what multiplication means. Area is arguably the most important physical application of this idea. Addition (length + width) is the wrong operation because it combines two measurements of different rows/columns rather than counting all squares across the entire grid.