A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?
A24 cm — multiply length times width
B11 cm — add length and width
C22 cm — add all four sides: 8 + 3 + 8 + 3
D22 cm² — add all four sides using square units
Perimeter is the sum of all sides. A rectangle has four sides — two lengths and two widths — so 8 + 3 + 8 + 3 = 22 cm. Option A (24 cm) is the area. Option B (11 cm) adds only one length and one width, forgetting that opposite sides are equal and must both be counted. Option D has the right number but the wrong unit — perimeter is measured in cm (linear), not cm² (area).
Question 2 Multiple Choice
Two rectangles both have a perimeter of 20 cm. Rectangle A is a square with sides of 5 cm. Rectangle B is 9 cm long and 1 cm wide. What can you conclude about their areas?
ATheir areas are equal because their perimeters are equal
BRectangle A has more area — 25 cm² vs. 9 cm² for Rectangle B
CRectangle B has more area because it is longer
DYou cannot compare their areas without measuring the perimeter again
Equal perimeters do NOT imply equal areas. Rectangle A (5 × 5) has area 25 cm². Rectangle B (9 × 1) has area 9 cm² — much less, despite the same perimeter. Perimeter measures distance around the boundary; area measures the region inside. A shape stretched thin can have a large perimeter while enclosing very little area. These are independent measurements.
Question 3 True / False
When finding the perimeter of a five-sided polygon, you must measure and add all five sides, even if two of them appear to be the same length.
TTrue
FFalse
Answer: True
Every side contributes to the perimeter, regardless of how sides look. Unless a diagram explicitly labels sides as equal (or the shape is a known regular polygon), you must measure each one individually. Stopping after the sides that look different, or skipping unlabeled sides, gives an incomplete and incorrect perimeter.
Question 4 True / False
A shape with a larger perimeter typically encloses a larger area than a shape with a smaller perimeter.
TTrue
FFalse
Answer: False
Perimeter and area are independent measurements. A very long, thin rectangle can have a large perimeter while enclosing a tiny area. For example, a 50 cm × 1 cm rectangle has perimeter 102 cm but area only 50 cm². A 10 cm × 10 cm square has perimeter 40 cm but area 100 cm² — smaller perimeter, larger area. The relationship between them depends entirely on the shape.
Question 5 Short Answer
A garden is shaped like a rectangle with a length of 10 m and a width of 2 m. Your friend says the perimeter is 12 m. What mistake did your friend make, and what is the correct perimeter?
Think about your answer, then reveal below.
Model answer: The friend added only one length and one width (10 + 2 = 12) instead of all four sides. A rectangle has two lengths and two widths, so the perimeter is 10 + 2 + 10 + 2 = 24 m. Equivalently: 2 × (10 + 2) = 2 × 12 = 24 m.
This is the most common perimeter error: treating a rectangle as if it only has two sides instead of four. Perimeter means the distance all the way around — you must traverse every side and return to the start. The shortcut 2 × (length + width) works because opposite sides of a rectangle are equal, but the student must first recognize that there are indeed four sides to account for.