Area
Definition
The measure of the two-dimensional space enclosed by a shape, expressed in square units (ft², m², etc.).
Why is Area Important?
Area is a foundational mathematical concept used across science, engineering, finance, and everyday problem-solving. From analyzing data sets to optimizing business decisions, this concept provides the analytical framework needed to interpret quantitative information accurately.
Our math calculators make complex computations simple and accessible, providing step-by-step results that help students, professionals, and curious minds explore mathematical relationships with confidence.
What is Area?
Area is the measure of the two-dimensional space enclosed by a shape, expressed in square units (ft², m², in², cm², acres, hectares). It answers: "How much surface does this shape cover?"
Area Formulas for Common Shapes
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = length × width | 10' × 12' = 120 ft² |
| Square | A = side² | 8' × 8' = 64 ft² |
| Triangle | A = ½ × base × height | ½ × 10' × 6' = 30 ft² |
| Circle | A = πr² | π × 5² = 78.54 ft² |
| Trapezoid | A = ½(b₁ + b₂) × h | ½(8+12) × 5 = 50 ft² |
| Parallelogram | A = base × height | 10' × 7' = 70 ft² |
| Ellipse | A = π × a × b | π × 6 × 4 = 75.4 ft² |
Area Unit Conversions
| From | To | Multiply By |
|---|---|---|
| 1 ft² | in² | 144 |
| 1 yd² | ft² | 9 |
| 1 acre | ft² | 43,560 |
| 1 m² | ft² | 10.764 |
| 1 hectare | acres | 2.471 |
| 1 mi² | acres | 640 |