What is the Difference Between Area and Perimeter?
Area measures the amount of surface enclosed within a 2D shape. It is always expressed in square units (cm², m², ft², etc.). Think of area as how much paint you need to cover a wall, or how much carpet to cover a floor.
Perimeter measures the total length of the boundary (all sides) of a shape. It is expressed in linear units (cm, m, ft, etc.). Think of perimeter as the length of fence needed to surround a garden, or the amount of ribbon to go around the edge of a picture frame.
Perimeter → linear units (cm, m, in, ft)
Complete Formula Reference Table
| Shape | Area Formula | Perimeter Formula |
|---|---|---|
| Circle | A = πr² | C = 2πr (circumference) |
| Rectangle | A = l × w | P = 2(l + w) |
| Square | A = s² | P = 4s |
| Triangle | A = ½ × b × h | P = a + b + c |
| Trapezoid | A = ½(a + b) × h | P = a + b + c + d |
| Parallelogram | A = b × h | P = 2(a + b) |
| Rhombus | A = ½ × d₁ × d₂ | P = 4s |
| Regular Hexagon | A = (3√3/2) × s² | P = 6s |
Circle – Area and Circumference
A circle is defined by its radius (r) — the distance from the center to any point on the edge. The diameter (d) = 2r. The mathematical constant π (pi) ≈ 3.14159.
Circumference = 2 × π × r = π × d
Worked Example
Find the area and circumference of a circle with radius 7 cm.
Circumference = 2 × π × 7 = 14π ≈ 43.98 cm
➡️ Use our Area of Circle Calculator or Circumference Calculator.
Rectangle – Area and Perimeter
A rectangle has four right angles with opposite sides equal. It needs two measurements: length (l) and width (w).
Perimeter = 2 × (Length + Width)
Diagonal = √(l² + w²)
Worked Example
A room is 8 m long and 5 m wide. Find its area and perimeter.
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 m
Practical use: To tile the floor, you need 40 m² of tiles. To install skirting board around the edge, you need 26 m.
➡️ Use our Area of Rectangle Calculator.
Square – Area and Perimeter
A square is a special rectangle where all sides (s) are equal.
Perimeter = 4s
Diagonal = s√2
Worked Example
A square garden plot has sides of 9 m.
Perimeter = 4 × 9 = 36 m
Diagonal = 9√2 ≈ 12.73 m
➡️ Use our Area of Square Calculator.
Triangle – Area and Perimeter
Triangles require different formulas depending on what information is available.
Method 2 (Heron's, 3 sides): s=(a+b+c)/2, Area=√(s(s-a)(s-b)(s-c))
Method 3 (SAS): Area = ½ × a × b × sin(C)
Perimeter = a + b + c
Worked Example
A triangle has base = 10 cm and height = 6 cm.
Heron's formula example: Triangle with sides 5 cm, 6 cm, 7 cm.
Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 cm²
Perimeter = 5+6+7 = 18 cm
➡️ Use our Area of Triangle Calculator.
Trapezoid – Area and Perimeter
A trapezoid has one pair of parallel sides called the bases (a and b), a height (h), and two non-parallel sides (c and d).
Perimeter = a + b + c + d
Worked Example
A trapezoid with parallel sides 8 cm and 12 cm, height 5 cm, and non-parallel sides 6 cm each.
Perimeter = 8 + 12 + 6 + 6 = 32 cm
Real-World Applications of Area and Perimeter
- Flooring: Calculate area (m² or ft²) to buy tiles, carpet, or hardwood floor.
- Fencing: Calculate perimeter to know how much fence to buy for a garden.
- Painting: Calculate wall area (length × height) to know how many cans of paint you need.
- Landscaping: Calculate lawn area to determine fertilizer quantities (often given per m²).
- Construction: Builders calculate floor areas to estimate material costs.
- Farming: Agricultural plots are measured in area (acres, hectares) to plan crop yields.
Quick Tips to Remember the Formulas
- Circle area: "Apple Pie R Squared" — A = πr²
- Rectangle area: Always length × width — just like counting grid squares
- Triangle area: Half of the rectangle with the same base and height — ½bh
- Perimeters: Always add ALL sides — just "walk around" the shape