Questions: Finding Perimeter of Rectangles and Squares

Question 1

A rectangle has a length of 7 cm and a width of 4 cm. What is its perimeter?

• A. 11 cm — add length and width
• B. 28 cm — multiply length by width
• C. 22 cm — add all four sides: 7 + 4 + 7 + 4
• D. 14 cm — double the length only

Answer: (C)

Perimeter is the total distance around all four sides. A rectangle with length 7 and width 4 has sides of 7, 4, 7, and 4 (opposite sides are equal). Adding all four: 7 + 4 + 7 + 4 = 22 cm. Option A only adds two sides. Option B (7 × 4 = 28) calculates area — the space inside — not the distance around. Option D only doubles one side. The formula 2 × (7 + 4) = 22 gives the same correct answer.

Question 2

A student computes 4 × 7 = 28 square centimeters for a rectangle with length 7 cm and width 4 cm. What measurement did the student calculate?

• A. Perimeter — the distance around the rectangle
• B. Area — the amount of space enclosed inside the rectangle
• C. Both area and perimeter — they are the same for rectangles
• D. Neither — you cannot use multiplication for rectangles

Answer: (B)

4 × 7 = 28 square centimeters is the area of the rectangle — how much surface is enclosed inside. Area is measured in square units (cm², m², ft²). Perimeter is 2 × 7 + 2 × 4 = 22 cm — the distance around the outside, measured in linear units (cm, m, ft). Confusing these two is one of the most persistent errors in geometry. They are different measurements, computed differently, used to answer different questions, and expressed in different units.

Question 3

For a rectangle with length 5 and width 3, the perimeter equals 5 + 3 = 8 units.

• T. True
• F. False

Answer: False

This is a very common error — adding only two sides instead of all four. A rectangle has four sides: two lengths and two widths. The perimeter is 5 + 3 + 5 + 3 = 16 units, or equivalently 2 × (5 + 3) = 16. Adding only length + width gives half the perimeter. Remember: perimeter is the distance all the way around the shape, which means you must account for every side.

Question 4

Perimeter is measured in linear units (like cm or feet), not square units.

• T. True
• F. False

Answer: True

Perimeter is a distance — how far you'd travel if you walked around the outside edge of a shape. Distance is measured in linear units: centimeters, meters, inches, feet. Area, by contrast, measures how much surface is enclosed, and is measured in square units (cm², m², ft²). Keeping this distinction clear matters for both calculation and interpretation: baseboard trim is measured in linear feet (perimeter), while carpet or flooring is measured in square feet (area).

Question 5

Why is the formula for the perimeter of a rectangle 2 × length + 2 × width, rather than just length × width?

Model answer: Because perimeter is the sum of all four sides, not a product of two sides. A rectangle has two sides equal to the length and two equal to the width. Adding all four gives length + width + length + width, which is the same as 2 × length + 2 × width. Multiplying length × width gives area — the space inside — which is a completely different measurement.

The formula 2l + 2w is just a compressed way of adding all four sides of a rectangle: l + w + l + w = 2l + 2w. It's useful because it reduces four additions to two multiplications, but it comes directly from the definition of perimeter. Length × width is the area formula — it counts how many unit squares fit inside. These two formulas answer two completely different geometric questions about the same shape.