Area Calculator — Find Area of 6 Common Shapes with Step-by-Step Solutions
Use the Area Calculator to find the area of rectangles, squares, triangles, circles, trapezoids, and parallelograms. See the formula, step-by-step working, and final answer for any shape. Includes worked examples, common mistakes, practice problems, and comprehensive FAQs. For related geometry tools, see our perimeter calculator.
Table of Contents
Area Calculator — Step-by-Step
Select a shape, enter its dimensions, and click Calculate. The calculator shows the formula and each calculation step.
What Is Area?
Area is the amount of space inside a two-dimensional shape. It answers: "How much flat surface does this shape cover?" Area is measured in square units (m², cm², ft², in²).
Area = space enclosed by a 2D shape Units = square (m², cm², ft²) 1 square unit = a square with sides of 1 unit.
Key points:
- Square units: Area always has squared units.
- Consistent units: Convert to the same unit first.
- Additive: Composite shapes = sum of parts.
- Never negative.
- Not perimeter: Area is space inside; perimeter is the boundary.
Area of a Rectangle
Rectangle Area Formula
A = l × w
Example: l=10, w=5 → A = 10 × 5 = 50 square units
Area of a Square
Square Area Formula
A = s²
Example: s=7 → A = 7² = 49 square units
Area of a Triangle
Triangle Area Formula
A = ½ × b × h
Example: b=10, h=6 → A = ½ × 10 × 6 = 30 square units
Area of a Circle
Circle Area Formula
A = πr²
Example: r=5 → A = π × 25 ≈ 78.54 square units (exact: 25π)
Area of a Trapezoid
Trapezoid Area Formula
A = ½ × (b₁ + b₂) × h
Example: b₁=8, b₂=12, h=5 → A = ½ × 20 × 5 = 50 square units
Area of a Parallelogram
Parallelogram Area Formula
A = b × h (perpendicular height, not slant side)
Example: b=10, h=4 → A = 40 square units
Common Mistakes to Avoid
- Using slant height instead of perpendicular height.
- Forgetting the ½ in triangle and trapezoid formulas.
- Confusing radius with diameter in circles.
- Mixing units.
- Not squaring units in the answer.
- Wrong trapezoid height — use perpendicular distance between bases.
Real-World Uses of Area
- Flooring: Carpet, tile, hardwood.
- Painting: Paint quantity estimation.
- Landscaping: Sod, mulch, paving.
- Construction: Roofing, siding, concrete.
- Real estate: Square footage valuation.
- Agriculture: Field measurement.
Practice Problems with Solutions
Problem 1: Rectangle l=12, w=7 → 84 cm²
Problem 2: Triangle b=15, h=8 → 60 m²
Problem 3: Circle r=6 → 36π ≈ 113.10 cm²
Problem 4: Trapezoid bases 10 & 14, h=6 → 72 sq units
Problem 5: Square 9m with circle r=2 removed → 68.43 m²
Summary & Next Steps
Master these six formulas for most geometry problems. Always use consistent units, perpendicular heights, and squared units.
13. Frequently Asked Questions
Multiply length by width: A = l × w. Example: l=10, w=5 → A = 50 square units.
A = ½ × b × h, where b is the base and h is the perpendicular height.
Use A = πr² with the radius. If you know the diameter, divide by 2 first.
Using slant height instead of perpendicular height, forgetting ½, confusing radius with diameter, mixing units, and forgetting squared units.
Area measures space inside (square units). Perimeter measures distance around (linear units).
A = ½ × (b₁ + b₂) × h. Add the parallel bases, multiply by perpendicular height, divide by 2.
A = b × h using perpendicular height, not the slant side.
Explore Math Topics
Continue your learning journey with our other math guides
Related Calculators
Explore these other geometry tools:
- 🔹 Perimeter Calculator — Find the distance around shapes.
- 🔹 Rectangle Calculator — Calculate rectangle dimensions.
- 🔹 Square Calculator — Calculate square properties.
- 🔹 Triangle Area Calculator — Dedicated triangle area tool.
- 🔹 Circle Area Calculator — Dedicated circle area tool.
- 🔹 Trapezoid Calculator — Calculate trapezoid properties.
Conclusion
Master these six area formulas and you'll handle most geometry problems. Use this calculator to verify your work, but practice applying the formulas until they become second nature.
Readers who wish to continue practicing and reinforce what they've learned can explore the companion learning resource for guided exercises.