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Area Formula
Area is the measurement of the two-dimensional space enclosed inside a boundary. Whether you are painting a wall, buying sod for a yard, or solving geometry homework, knowing how to calculate area is a critical skill. For quick answers, use the area calculator or the square footage calculator to find the coverage of any space in seconds.
8 min read
What is the area formula?
Unlike 1-dimensional measurements like length or perimeter, area measures coverage in 2-dimensional space. Because different shapes fill space in different ways, there is no single universal formula for area. Instead, each geometric shape has its own formula.
All area formulas multiply two linear measurements (like length and width) and express the final result in square units (e.g., square meters, square inches, or square feet).
Common 2D Area Formulas
Here are the standard formulas for the most common two-dimensional geometric shapes:
| Shape | Formula | Variables Explained |
|---|---|---|
| Square | A = s² | s = side length |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½ × b × h | b = base, h = height (perpendicular) |
| Circle | A = π × r² | r = radius, π ≈ 3.14159 |
| Trapezoid | A = ½ × (a + b) × h | a, b = parallel bases, h = height |
| Parallelogram | A = b × h | b = base, h = height (perpendicular) |
Worked Examples: Step-by-Step Calculations
Let's calculate the area for each of these shapes using real numbers.
1. Area of a Square
Calculate the area of a square concrete slab with side lengths of 5 meters.
- Formula: A = s²
- Calculation: A = 5² = 5 × 5
- Result: A = 25 m²
2. Area of a Rectangle
Find the area of a garden bed that is 12 feet long and 4 feet wide.
- Formula: A = l × w
- Calculation: A = 12 × 4
- Result: A = 48 sq ft
3. Area of a Triangle
Find the area of a triangular sail with a base of 6 yards and a height of 8 yards.
- Formula: A = ½ × b × h
- Calculation: A = 0.5 × 6 × 8
- Result: A = 24 sq yd
4. Area of a Circle
Calculate the area of a circular rug with a radius of 3 feet (use π ≈ 3.14159).
- Formula: A = π × r²
- Calculation: A = 3.14159 × 3² = 3.14159 × 9
- Result: A ≈ 28.27 sq ft
5. Area of a Trapezoid
Find the area of a trapezoidal plot with parallel bases of 10 feet and 14 feet, and a perpendicular height of 5 feet.
- Formula: A = ½ × (a + b) × h
- Calculation: A = 0.5 × (10 + 14) × 5 = 0.5 × 24 × 5
- Result: A = 60 sq ft
6. Area of a Parallelogram
Calculate the area of a parallelogram with a base of 9 inches and a height of 4 inches.
- Formula: A = b × h
- Calculation: A = 9 × 4
- Result: A = 36 sq in
Common Area Calculation Mistakes
- Using slanted side lengths instead of height. In triangles, trapezoids, and parallelograms, the height must be measured perpendicular (at a 90-degree angle) to the base. Slanted sides are longer and will skew the result if used incorrectly.
- Mixing up radius and diameter. For the area of a circle (πr²), you must use the radius. If you are given the diameter, divide it by 2 first. Squaring the diameter will give an area that is 4 times too large!
- Forgetting to convert units first. If a room is 10 feet long and 96 inches wide, you cannot just multiply 10 by 96. Convert 96 inches to 8 feet first, then multiply (10 × 8 = 80 square feet).
- Forgetting the fraction multiplier. In triangles and trapezoids, don't forget to multiply by ½ (or divide by 2) at the end of the calculation.
Run the numbers
Use our interactive geometry and construction tools to calculate areas instantly: