Parallelogram
Find the area, perimeter, diagonals, heights and angles of a parallelogram from a side and height, two sides and an angle, or the diagonals and angle.
The parallelogram calculator finds the area, perimeter, diagonals, heights and angles of a parallelogram. It can be given by a side and its height, two sides and the included angle, the diagonals and the angle between them, or two sides and a diagonal.
Area formulas
| What is known | Formula |
|---|---|
| Side and height | S = a · ha |
| Two sides and an angle | S = a · b · sin α |
| Diagonals and the angle between them | S = ½ · d1 · d2 · sin φ |
Diagonals and sides
The diagonals are found with the law of cosines: d1² = a² + b² − 2ab cos α, d2² = a² + b² + 2ab cos α.
The sum of the squares of the diagonals equals the sum of the squares of all sides: d1² + d2² = 2(a² + b²).
Example. a = 10 cm, b = 6 cm, α = 30°.
S = 10 · 6 · sin 30° = 30 cm², P = 2 · (10 + 6) = 32 cm
d1 = √(100 + 36 − 120 · cos 30°) ≈ 5.66 cm, d2 ≈ 15.49 cm
Properties of a parallelogram
- Opposite sides are equal and parallel, opposite angles are equal.
- Adjacent angles add up to 180°.
- The diagonals bisect each other and divide the parallelogram into four triangles of equal area.
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