Area and perimeter formulas
Square, rectangle, circle, triangle: the area and perimeter formulas for the most common shapes.
Common shapes
| Shape | Area | Perimeter |
|---|---|---|
| Square | side² | 4 × side |
| Rectangle | length × width | 2 × (length + width) |
| Triangle | (base × height) / 2 | sum of the 3 sides |
| Circle | π × radius² | 2 × π × radius |
| Parallelogram | base × height | 2 × (side a + side b) |
| Trapezoid | ((base 1 + base 2) × height) / 2 | sum of the 4 sides |
π (pi) is approximately 3.14159 — for a quick calculation, 3.14 is close enough for the vast majority of practical cases.
Triangle: special cases
| Type | Area formula |
|---|---|
| Right triangle | (leg 1 × leg 2) / 2, the two sides forming the right angle |
| Equilateral triangle | (side² × √3) / 4 |
Heron's formula (area from the 3 sides)
s = (a + b + c) / 2 (semi-perimeter) Area = √(s × (s−a) × (s−b) × (s−c))
Useful when you know a triangle's 3 sides but not its height.
Circle: radius, diameter, circumference
Diameter = 2 × radius Circumference = π × diameter = 2 × π × radius Area = π × radius²
Sector and arc of a circle
Arc length = (angle in degrees / 360) × 2 × π × radius Sector area = (angle in degrees / 360) × π × radius²
A circular sector is the "pie slice" bounded by a central angle — its arc length and area are simply the corresponding fraction of the full circle.
Regular polygon (n sides)
Perimeter = n × side length Area = (Perimeter × apothem) / 2
The apothem is the distance from the centre to the midpoint of a side (perpendicular to it) — the more sides a polygon has, the closer it gets to a circle.
A worked example
A rectangular garden, 8 m × 5 m, with a circular roundabout of 2 m radius at its centre:
Rectangle area = 8 × 5 = 40 m² Circle area = π × 2² ≈ 12.57 m² Remaining lawn area ≈ 40 − 12.57 = 27.43 m²
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