A circle of radius 3 has an area of πr² = 28.27; a sphere of radius 3 has a volume of (4/3)πr³ = 113.10.
| Shape | Area or surface area | Perimeter or volume | Example | Area | Perimeter or volume |
|---|---|---|---|---|---|
| Square | A = a² | P = 4a | a = 4 | 16.00 | 16.00 |
| Rectangle | A = l × w | P = 2(l + w) | l = 4, w = 3 | 12.00 | 14.00 |
| Right triangle | A = ½ b × h | P = b + h + √(b² + h²) | b = 3, h = 4 | 6.00 | 12.00 |
| Circle | A = πr² | C = 2πr | r = 3 | 28.27 | 18.85 |
| Isosceles trapezoid | A = ½ (a + b) × h | P = a + b + 2c | a = 6, b = 4, c = 3 | 14.14 | 16.00 |
| Parallelogram | A = b × h | P = 2(a + b) | b = 6, a = 5, h = 4 | 24.00 | 22.00 |
| Rhombus | A = (d₁ × d₂) ÷ 2 | P = 2√(d₁² + d₂²) | d₁ = 6, d₂ = 8 | 24.00 | 20.00 |
| Ellipse | A = πab | P ≈ π[3(a + b) − √((3a + b)(a + 3b))] | a = 5, b = 3 | 47.12 | 25.53 |
| Regular hexagon | A = (3√3 ÷ 2) a² | P = 6a | a = 2 | 10.39 | 12.00 |
| Cube | S = 6a² | V = a³ | a = 3 | 54.00 | 27.00 |
| Rectangular box | S = 2(lw + lh + wh) | V = l × w × h | l = 4, w = 3, h = 2 | 52.00 | 24.00 |
| Sphere | S = 4πr² | V = (4/3)πr³ | r = 3 | 113.10 | 113.10 |
| Cylinder | S = 2πr(r + h) | V = πr²h | r = 2, h = 5 | 87.96 | 62.83 |
| Cone | S = πr(r + √(r² + h²)) | V = (1/3)πr²h | r = 3, h = 4 | 75.40 | 37.70 |
| Square pyramid | S = a² + 2a√(a²/4 + h²) | V = (1/3)a²h | a = 4, h = 3 | 44.84 | 16.00 |
How it is computed
Each example plugs the listed dimensions into the formula on the same row, with π to full precision, and rounds the result to two decimals. Units are whatever you measure in: centimetres give cm² and cm³. The ellipse perimeter uses Ramanujan's approximation, accurate to a fraction of a percent.
FAQ
What is the difference between area and surface area?+
Area measures a flat shape. Surface area adds up every face of a solid, the amount of paint or wrapping it would take.
Why does the ellipse perimeter use ≈?+
An ellipse's exact perimeter has no simple closed formula. Ramanujan's approximation is within a fraction of a percent for everyday shapes.