Area and perimeter of common shapes
The area measures the surface inside a shape, in square units; the perimeter is the length of its outline. You need the area to buy paint, flooring or fabric, and the perimeter for edging, trim or fencing. This calculator covers eight flat shapes; circles, triangles and regular polygons have their own calculators.
The formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length × width | 2 × (length + width) |
| Square | side² | 4 × side |
| Parallelogram | base × height | 2 × (base + slanted side) |
| Trapezoid | (long base + short base) ÷ 2 × height | sum of the four sides |
| Rhombus | diagonal 1 × diagonal 2 ÷ 2 | 2 × √(d1² + d2²) |
| Ellipse | π × a × b | approximately π(a + b)(1 + 3h ÷ (10 + √(4 − 3h))) with h = (a − b)² ÷ (a + b)² |
| Semicircle | π × r² ÷ 2 | π × r + 2r |
| Ring | π × (R² − r²) | 2π × (R + r) |
For an isosceles trapezoid, each slanted leg is √(height² + ((long base − short base) ÷ 2)²).
Worked examples
- Rectangle 12 × 8: area 12 × 8 = 96, perimeter 2 × 20 = 40, diagonal √(144 + 64) = 14.42.
- Trapezoid with bases 10 and 6 and height 4: area (10 + 6) ÷ 2 × 4 = 32. Each leg is √(16 + 4) = 4.47, so the perimeter is 10 + 6 + 8.94 = 24.94.
- Ellipse with semi-axes 5 and 3: area π × 15 = 47.12, perimeter about 25.53.
- Ring with radii 5 and 3: area π × (25 − 9) = 50.27.
Rectangle area as the length changes (width 8)
| Length | Area | Perimeter |
|---|---|---|
| 4 | 32 | 24 |
| 8 | 64 | 32 |
| 12 | 96 | 40 |
| 16 | 128 | 48 |
| 20 | 160 | 56 |
Doubling one side doubles the area, but doubling both sides multiplies it by four.
Tips
- Keep units consistent. Measure every side in the same unit. The area comes out in that unit squared: feet give square feet, centimeters give square centimeters.
- Split complex shapes. An L-shaped room is two rectangles; a garden bed with a rounded end is a rectangle plus a semicircle. Add the areas, and add only the outer edges for the perimeter.
- Height is perpendicular. For parallelograms and trapezoids, use the straight-up height, not the slanted side, or the area will be too large.
- The ellipse perimeter is an approximation. There is no simple exact formula; Ramanujan’s is accurate to far better than 0.01% for everyday shapes.