Area Calculator
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Circle Area
Area Calculation Results
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Area is measured in square units (cm², m², in², ft²). All calculations use standard mathematical formulas. Results are rounded to 2 decimal places. Different units available: Centimeters, Meters, Inches, Feet.
Complete Area Calculation Guide
Area is the amount of space inside a two-dimensional shape. This guide explains how to calculate area for various geometric shapes and provides formulas, examples, and practical applications.
Area Formulas for Common Shapes
| Shape | Formula | Variables | Example |
|---|---|---|---|
| Circle | A = πr² | r = radius | r=5 → A=78.54 |
| Rectangle | A = l × w | l = length, w = width | 10×5 → A=50 |
| Triangle | A = ½ × b × h | b = base, h = height | 8×6 → A=24 |
| Square | A = s² | s = side | s=5 → A=25 |
| Trapezoid | A = ½ × (b₁+b₂) × h | b₁, b₂ = bases, h = height | (10+6)×5÷2 → A=40 |
| Ellipse | A = π × a × b | a, b = semi-axes | a=7, b=4 → A=87.96 |
| Parallelogram | A = b × h | b = base, h = height | 8×6 → A=48 |
| Rhombus | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals | 10×8÷2 → A=40 |
Unit Conversion for Area
| From | To | Multiply By |
|---|---|---|
| cm² | m² | 0.0001 |
| m² | cm² | 10,000 |
| in² | ft² | 0.00694 |
| ft² | in² | 144 |
| cm² | in² | 0.155 |
| m² | ft² | 10.764 |
Real-World Area Calculation Examples
- Painting a Room: Wall area = 10ft × 8ft = 80 ft². Need paint for 80 sq feet
- Lawn Area: Rectangular yard 20m × 15m = 300 m². Know exactly how much fertilizer needed
- Pizza Size: 12" diameter pizza: A = π × 6² = 113.1 in². Larger area = more toppings
- Floor Tiling: Kitchen 12ft × 10ft = 120 ft². Need 120 ÷ (tile area) tiles
- Circular Pool: 5m radius pool: A = π × 5² = 78.5 m². Know volume of water (depth × area)
Area Calculation Tips
- Measure Accurately: Small measurement errors become larger in area (squared)
- Use Consistent Units: Convert all measurements to same unit before calculating
- Height vs Side: Height for triangles/trapezoids is perpendicular, not slant
- Radius vs Diameter: Circle area uses radius, not diameter (radius = diameter ÷ 2)
- Complex Shapes: Break into simpler shapes, calculate each, then add together
Geometric Shape Definitions
- Circle: All points equidistant from center. A = πr²
- Rectangle: Four right angles, opposite sides equal. A = length × width
- Triangle: Three sides and angles. A = ½ × base × height
- Square: Rectangle with all sides equal. A = side²
- Trapezoid: One pair of parallel sides. A = ½ × (base₁ + base₂) × height
- Ellipse: Oval shape with two axes. A = π × semi-major × semi-minor
- Parallelogram: Opposite sides parallel and equal. A = base × height
- Rhombus: Parallelogram with all sides equal. A = ½ × diagonal₁ × diagonal₂
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Frequently Asked Questions
1. What is area?
Area is the amount of space inside a two-dimensional shape. Measured in square units like cm², m², in², ft². For example, a 5cm × 5cm square has area 25 cm².
2. What's difference between radius and diameter?
Radius is distance from center to edge. Diameter is distance across (center to opposite edge). Diameter = 2 × radius. Circle area uses radius: A = πr².
3. How do I find height of triangle?
Height is perpendicular distance from base to opposite vertex. Draw line perpendicular to base. Can use Pythagorean theorem if given sides instead of height.
4. What's difference between area and perimeter?
Area is space inside (square units). Perimeter is distance around edge (linear units). Example: 5×5 square has area 25 cm² and perimeter 20 cm.
5. How do I calculate area of irregular shapes?
Break into smaller regular shapes (squares, triangles, etc.). Calculate area of each. Add together for total. Or use approximation grid method.
6. What unit should I use?
Use consistent unit for all measurements. Then area is in that unit squared. Example: measures in cm → area in cm². Convert if needed afterward.
7. How do I convert cm² to m²?
Divide by 10,000. (1 m = 100 cm, so 1 m² = 100² = 10,000 cm²). Example: 50,000 cm² = 5 m².
8. What's π (pi) value?
π ≈ 3.14159... (infinite decimals). For circle area: A = πr². Most calculations use 3.14 or 3.14159 for accuracy.
9. How do I find area with only angles?
Can't calculate area from angles alone. Need at least one measurement (side length or height). Angles tell shape but not size.
10. Can area be zero?
Only if shape has no dimensions. A line (no width) has zero area. All 2D shapes with length and width have positive area.
11. What's semi-major axis?
For ellipse: semi-major axis is half the longest diameter (a). Semi-minor axis is half the shortest diameter (b). Area = π × a × b.
12. How do I calculate area of trapezoid?
Average the two bases, multiply by height: A = ½ × (base₁ + base₂) × height. Example: bases 10&6, height 5 → ½ × 16 × 5 = 40 sq units.