Questions: Perimeter

Question 1

A farmer wants to put a fence around a rectangular garden that is 12 meters long and 8 meters wide. How much fencing does she need?

• A. 96 meters — multiply length × width to find the total space to fence
• B. 20 meters — add the length and width once
• C. 40 meters — add all four sides: 12 + 8 + 12 + 8
• D. 48 meters — use the formula P = l × w ÷ 2

Answer: (C)

Perimeter is the total distance around the shape — all four sides added together. A rectangle has two sides of each length, so 12 + 8 + 12 + 8 = 40 meters. Option A (96 m) is the area mistake — 12 × 8 = 96 tells you how much soil to buy, not how much fencing. Fencing follows the boundary, not the interior.

Question 2

A rectangle has a perimeter of 28 cm and a length of 9 cm. What is its width?

• A. 19 cm
• B. 5 cm
• C. 10 cm
• D. 14 cm

Answer: (B)

Use P = 2l + 2w: 28 = 2(9) + 2w → 28 = 18 + 2w → 10 = 2w → w = 5 cm. A common error is subtracting 9 from 28 and getting 19, which forgets that perimeter counts both lengths and both widths — not just one of each.

Question 3

The perimeter of a rectangle is measured in square units, just like area.

• T. True
• F. False

Answer: False

Perimeter is a linear (one-dimensional) measurement — it counts the total length around the boundary, so it uses units like cm, m, or inches. Square units (cm², m²) are used for area, which measures the interior space. This is one of the most important distinctions between the two concepts.

Question 4

To find the perimeter of any polygon, you always add up the lengths of all its sides.

• T. True
• F. False

Answer: True

This general method works for every polygon — triangles, rectangles, irregular hexagons, and any other shape with straight sides. The rectangle shortcut P = 2l + 2w is just a faster version of adding all four sides when you know opposite sides are equal. The underlying rule is always: sum all side lengths.

Question 5

What is the difference between perimeter and area? Give a real-world example of a situation where you would need to calculate each.

Model answer: Perimeter is the total length around the outside boundary of a shape, measured in linear units (cm, m). Area is the amount of space inside a shape, measured in square units (cm², m²). Example: you'd calculate perimeter to find how much fencing to enclose a yard; you'd calculate area to find how much carpet to cover that yard's floor.

Same yard, completely different questions. Perimeter answers 'how long is the path around it?' — relevant for fencing, framing, or ribbon. Area answers 'how much space is inside?' — relevant for flooring, painting, or seeding. Confusing the two leads to real-world errors, like buying 96 meters of fencing for a yard that only needs 40.