Area and perimeter
The idea
Perimeter measures distance around a boundary; area measures surface covered. Their units differ: length units for perimeter and square units for area. Shapes with the same perimeter can have different areas.
Worked example
A 3 cm by 5 cm rectangle has perimeter 2 × (3 + 5) = 16 cm and area 3 × 5 = 15 square centimeters. A 2 cm by 6 cm rectangle also has perimeter 16 cm, but area 12 square centimeters.
Another application
A square with side 5 units has area 25 square units and perimeter 20 units. Doubling every side gives area 100 square units and perimeter 40 units: area scales differently from perimeter.
A common misunderstanding
Multiplying side lengths measures area, not distance around the edge. The unit attached to the answer helps distinguish the two quantities.
Try it yourself
On grid paper, draw three rectangles with perimeter 20 units. Compare their areas and explain which has the greatest area.
Check your understanding
What are the area and perimeter of a 4 by 7 rectangle?
Reveal the explained answer
Area 28 square units; perimeter 22 units.