A = bh
Area
Area equals base multiplied by perpendicular height.
NUT ENGINEERING TOOLS
Parallelogram Solver
See It. Solve It. Understand It.
Solve parallelogram area, height, perimeter, side length, interior angle, and diagonals from the measurements you know.
Live Geometry
Diagram updates when enough geometry is known.
Enter What You Know
Enter a supported combination of measurements. Leave unknown values blank.
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Calculated Results
Complete parallelogram geometry from the values you entered.
Base
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Side
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Height
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Interior Angle
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Area
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Perimeter
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Diagonal 1
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Diagonal 2
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Your Solution
Nut shows the equations and values used to solve the parallelogram.
Enter known measurements and solve the parallelogram to see the steps.
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How It Works
Parallelogram dimensions are related through area, perimeter, trigonometry, and the law of cosines.
P = 2(b + s)
Perimeter
Opposite sides of a parallelogram are equal.
h = s sin(θ)
Height
Height is the perpendicular component of the sloped side.
d₁ = √(b² + s² + 2bs cos θ)
Long Diagonal
One diagonal follows the law of cosines using the supplementary angle.
d₂ = √(b² + s² − 2bs cos θ)
Short Diagonal
The second diagonal follows the law of cosines using the interior angle.
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