Area and Perimeter Formulas
Rectangle
- Area = length × width
- Perimeter = 2 × (length + width)
Rectangles are the most common shape in construction and design. A square is a special rectangle where all four sides are equal.
Circle
- Area = π × r²
- Perimeter (Circumference) = 2 × π × r
Where r is the radius (distance from center to edge). The diameter is twice the radius. Pi (π) is approximately 3.14159265.
Triangle (Heron's Formula)
When you know all three sides but not the height, Heron's formula calculates the area:
- Semi-perimeter (s) = (a + b + c) ÷ 2
- Area = √(s × (s-a) × (s-b) × (s-c))
- Perimeter = a + b + c
The three sides must satisfy the triangle inequality: the sum of any two sides must be greater than the third side. This calculator validates that before computing.
Common Applications
| Use Case | Shape | What You Need |
|---|---|---|
| Flooring a room | Rectangle | Room length and width |
| Painting a wall | Rectangle | Wall height and width |
| Laying a circular patio | Circle | Radius or diameter |
| Fencing a triangular garden | Triangle | Three side lengths |
| Wrapping a pipe | Circle | Radius for circumference |
| Tiling a roof | Triangle | Base and height, or three sides |