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Parallelogram & Rhombus Calculator

Compute area, perimeter, height, and diagonals of a parallelogram or rhombus.

Parallelogram & rhombus formulas

Area (base & height)A = b × h
Area (sides & angle)A = a × b × sin θ
PerimeterP = 2(a + b)
Diagonalsp, q = √a2 + b2 ± 2ab cos θ
Rhombus areaA = p × q2
Rhombus perimeterP = 4a

Where a, b = side lengths, h = height to base b, θ = angle between sides, p, q = diagonals

Worked examples

  1. A parallelogram has sides 10 and 6 with a 60° angle between them. Find the height, area, perimeter and diagonals.

    1. h = 6 × sin 60° ≈ 5.196
    2. A = 10 × 5.196 ≈ 51.96
    3. P = 2(10 + 6) = 32
    4. long diagonal = √100 + 36 + 2·10·6·cos 60° = √196 = 14
    5. short diagonal = √136 − 60 = √76 ≈ 8.718

    Answer: A ≈ 51.96, P = 32, diagonals 14 and ≈ 8.72

  2. A rhombus has diagonals of 8 cm and 6 cm. Find its area, side and perimeter.

    1. A = 8 × 62 = 24
    2. The diagonals bisect each other at right angles, so side = √42 + 32 = 5
    3. P = 4 × 5 = 20

    Answer: A = 24 cm², side = 5 cm, P = 20 cm

Tips & common mistakes

  • The height is perpendicular to the base — not the slanted side.
  • Check: p² + q² = 2(a² + b²) for any parallelogram.