Common Mistakes: Area & Perimeter
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Area and perimeter are easy to mix up! Let's learn about common mistakes so you can avoid them.
Mistake #1: Confusing Area and Perimeter
Wrong: Finding the area when asked for perimeter (or vice versa)
Example: "What is the perimeter of a 5 x 3 rectangle?" Answer: 15
Right: Perimeter = 2(5) + 2(3) = 10 + 6 = 16 units
Remember: Perimeter = distance around (add sides). Area = space inside (multiply).
Mistake #2: Forgetting Units
Wrong: "The area is 24" (no units)
Right: "The area is 24 square feet" or "24 sq ft"
Area uses SQUARE units. Perimeter uses regular units.
Mistake #3: Only Adding Two Sides for Perimeter
Wrong: Perimeter of 8 x 5 rectangle = 8 + 5 = 13
Right: Perimeter = 8 + 5 + 8 + 5 = 26 (or 2 x 8 + 2 x 5 = 26)
A rectangle has 4 sides - count them all!
Practice: Find the Mistake
1. A student calculated the perimeter of a 6 x 4 rectangle as 24. What did they do wrong?
A) Nothing, 24 is correct
B) They found the area instead of perimeter
C) They added wrong
D) They multiplied wrong
Answer
B) - They multiplied (6 x 4 = 24) which is area. Perimeter = 2(6) + 2(4) = 20.
2. A student wrote "The area of the room is 35 feet." What's missing?
A) Nothing is missing
B) The word "square" - should be "35 square feet"
C) The length
D) The width
Answer
B) - Area is measured in SQUARE units. It should be "35 square feet."
3. To find the perimeter of a rectangle, you should:
A) Multiply length times width
B) Add length plus width
C) Add all four sides (or 2L + 2W)
D) Multiply all four sides
Answer
C) - Perimeter means adding all sides: L + W + L + W = 2L + 2W.
4. A student says a 3 x 3 square has perimeter 9. What's the correct perimeter?
A) 9
B) 6
C) 12
D) 36
Answer
C) 12 - The student found the area (3 x 3 = 9). Perimeter = 3 + 3 + 3 + 3 = 12.
5. When would you use area instead of perimeter?
A) Buying a fence for a yard
B) Buying carpet for a floor
C) Putting ribbon around a box
D) Walking around a track
Answer
B) - Carpet covers the inside (area). The others involve going around the edge (perimeter).
6. What is the correct unit for the perimeter of a room measured in feet?
A) Square feet
B) Feet
C) Cubic feet
D) Feet squared
Answer
B) Feet - Perimeter is a length (distance around), not an area.
7. A rectangle has an area of 20 square units. Could its dimensions be 5 x 5?
A) Yes
B) No, 5 x 5 = 25
C) No, 5 + 5 = 10
D) Maybe
Answer
B) - 5 x 5 = 25, not 20. Dimensions could be 4 x 5 or 2 x 10.
8. A student found the perimeter of a 7 x 3 rectangle by doing 7 + 3 = 10. What did they forget?
A) Nothing, that's correct
B) To multiply
C) That a rectangle has 4 sides, not 2
D) To subtract
Answer
C) - They only added 2 sides. Perimeter = 7 + 3 + 7 + 3 = 20.
9. Two rectangles both have perimeter 16. Must they have the same area?
A) Yes, same perimeter means same area
B) No, different dimensions can give different areas
C) Yes, perimeter equals area
D) You can't tell
Answer
B) - A 4x4 square has perimeter 16 and area 16. A 6x2 rectangle has perimeter 16 but area 12.
10. What's the key word that helps you know to find perimeter?
A) Cover
B) Fill
C) Around or border
D) Inside
Answer
C) - "Around" and "border" signal perimeter. "Cover," "fill," and "inside" signal area.
Next Steps
- Always ask: "Am I finding the distance around or the space inside?"
- Remember to use square units for area
- Count all four sides for perimeter
- Continue to the Unit Quiz