OneTaskBy Tim King · Updated
Area Calculator
Area of a Triangle, Trapezoid, Parallelogram, Kite and Circle, With Working
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How the Area Calculator works
This area calculator works out the area of eleven common flat shapes: squares, rectangles, triangles, circles, ellipses, trapezoids, parallelograms, rhombuses and kites, sectors and regular polygons. Pick a shape, type its measurements in any unit, and you get the area in that unit squared with the formula and every step shown.
Area is the amount of flat surface a shape covers, measured in square units. A rectangle 8 m by 5 m covers 40 square metres because forty 1 m squares fit inside it. Every other formula is a variation on that idea: a triangle is half a rectangle, a parallelogram is a rectangle with one end sliced off and moved, and a trapezoid is the average of its two parallel sides times its height.
How the area calculator works
Each shape uses its standard formula, shown alongside the answer. For a triangle where you only know the three sides, the calculator uses Heron's formula: find the half-perimeter s, then take √(s(s − a)(s − b)(s − c)). For a regular polygon it uses n × s² ÷ (4 × tan(180° ÷ n)), which works for any number of equal sides.
First example. A trapezoid with parallel sides of 6 and 10 and a height of 4 has an area of ½ × (6 + 10) × 4 = 32 square units.
Second example. A triangle with sides of 7, 8 and 9 has s = 12, so its area is √(12 × 5 × 4 × 3) = √720 ≈ 26.83.
How many tiles cover a 3.6 m by 2.4 m floor with 30 cm square tiles? The floor is 8.64 m² and each tile is 0.09 m², so you need 96 tiles before allowing for cuts.
Area formulas for common shapes, each with a worked size
| Shape | Formula | Dimensions | Area |
|---|---|---|---|
| Square | A = s² | s = 4 | 16 |
| Square | A = s² | s = 12 | 144 |
| Rectangle | A = l × w | l = 8, w = 5 | 40 |
| Rectangle | A = l × w | l = 20, w = 3.5 | 70 |
| Triangle (base and height) | A = ½ × b × h | b = 10, h = 6 | 30 |
| Triangle (base and height) | A = ½ × b × h | b = 7, h = 4 | 14 |
| Triangle (three sides) | A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2 | a = 3, b = 4, c = 5 | 6 |
| Triangle (three sides) | A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2 | a = 7, b = 8, c = 9 | 26.83 |
| Circle | A = πr² | r = 1 | 3.14 |
| Circle | A = πr² | r = 5 | 78.54 |
| Ellipse | A = π × a × b | a = 6, b = 4 | 75.4 |
| Ellipse | A = π × a × b | a = 10, b = 3 | 94.25 |
| Trapezoid | A = ½ × (a + b) × h | a = 6, b = 10, h = 4 | 32 |
| Trapezoid | A = ½ × (a + b) × h | a = 3, b = 9, h = 5 | 30 |
| Parallelogram | A = b × h | b = 9, h = 4 | 36 |
| Rhombus or kite (diagonals) | A = ½ × p × q | p = 10, q = 6 | 30 |
| Sector | A = (θ ÷ 360) × πr² | r = 6, degrees = 90 | 28.27 |
| Sector | A = (θ ÷ 360) × πr² | r = 10, degrees = 45 | 39.27 |
| Regular polygon | A = n × s² ÷ (4 × tan(180° ÷ n)) | n = 5, s = 4 | 27.53 |
| Regular polygon | A = n × s² ÷ (4 × tan(180° ÷ n)) | n = 6, s = 4 | 41.57 |
| Regular polygon | A = n × s² ÷ (4 × tan(180° ÷ n)) | n = 8, s = 4 | 77.25 |
| Regular polygon | A = n × s² ÷ (4 × tan(180° ÷ n)) | n = 12, s = 1 | 11.2 |
Tips
- Use the perpendicular height. For triangles, parallelograms and trapezoids, the height is measured at right angles to the base, not along the sloping side.
- Keep units consistent. Mixing centimetres and metres gives nonsense; convert first.
- Split awkward shapes. An L-shaped room is two rectangles. Work out each and add them.
FAQ
How do you find the area of a triangle without the height?
Use Heron's formula with the three side lengths. Add the sides and halve the total to get s, then multiply s by s minus each side in turn and take the square root. Choose "Triangle (three sides)" and the calculator does all of this and shows each step.
What is the area of a trapezoid?
Add the two parallel sides, halve the total and multiply by the perpendicular height between them. A trapezoid with parallel sides of 3 and 9 and a height of 5 has an area of 6 × 5 = 30. The two slanted sides do not appear in the formula at all.
How do you find the area of an irregular shape?
Break it into shapes you can measure, such as rectangles, triangles and sectors, work out each area with this calculator and add them together. For a shape with a cut-out, subtract the hole. For land with many corners, a coordinate method such as the shoelace formula is quicker.
Why is area measured in square units?
Area counts how many unit squares fit inside a shape. Multiplying two lengths, such as metres by metres, gives square metres. That is also why scaling a shape by two in every direction makes its area four times larger, not twice as large, which matters when pricing materials.
See also: all Algebra and Geometry tools, Arithmetic, Number Theory, Statistics, Trigonometry and Calculus.
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