Parallelogram Area from Two Sides and Angle

Find the area of a parallelogram from two sides and the included angle using ab sin θ. Also shows the perimeter and both diagonals with a scaled diagram.

Input

Enter two sides and the included angle to compute the parallelogram area as ab sin θ. The perimeter and both diagonals are also shown.

Side a

Side b

Included angle θ

Angle unit

Result

Area

20.78461

Perimeter

Diagonal (across angle)

5.291503

Diagonal (opposite)

8.717798

Lengths use the same unit as the inputs, and the area is in that unit squared.

How it works

The area uses the two side lengths a and b and the included angle θ as area = a × b × sin θ.
The included angle can be entered in degrees (greater than 0 and less than 180) or radians (greater than 0 and less than pi).
The perimeter is 2(a + b).
The diagonals come from the law of cosines. The one across the included angle is √(a² + b² − 2ab cos θ) and the other is √(a² + b² + 2ab cos θ).
Lengths use the same unit as the inputs, and the area is in that unit squared.

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