Perimeter
“Perimeter is the length once around the edge.”
The formula
▭ P = 2 × (a + b) ⬛ P = 4 × aHow to read it: A rectangle's perimeter is twice (width + height); a square's is four times one side
- a
- — the width (or one side of a square)
- b
- — the height
The hook
How far do you walk around a field once? The perimeter is the length all the way around the edge.
In plain words
The total length of the outline once around — just add up all the sides.
The intuition
Walk each side and add every length — that's the perimeter. A rectangle has two widths and two heights, so add (width+height) twice; a square has four equal sides, so take one side times 4.
How it's built
For any shape, perimeter = sum of all side lengths. In a rectangle the opposite sides match, so you can shortcut it to 2 × (width + height).
Example
Rectangle 5 by 3: 2 × (5 + 3) = 2 × 8 = 16.
Common mistake
Perimeter is not area. Perimeter is the edge length (cm); area is the space inside (cm²). Two shapes can share a perimeter but have different areas.
Where it's used
Fencing, picture-frame trim, running tracks, molding around a room.
Where it came from
'Peri-meter' comes from Greek for 'measure (meter) around (peri)'.
Quick check
What is the perimeter of a square with side 4?
- 8
- 12
- 16✓
- 20
Practice
Find the perimeter of a rectangle 6 by 2.
Answer: 16
- Perimeter = 2 × (width + height)
- 2 × (6 + 2) = 2 × 8 = 16
Takeaway: Rectangle perimeter is twice (width + height).
Find the perimeter of a triangle with sides 3, 4, 5.
Answer: 12
- Add all the sides.
- 3 + 4 + 5 = 12
Takeaway: Perimeter is the sum of every side.
Find the perimeter of a square with side 7.
Answer: 28
- A square has 4 equal sides.
- 7 × 4 = 28
Takeaway: Square perimeter = side × 4.