Parallelogram Area Calculator

Calculate the area, perimeter, diagonals, and angles of a parallelogram from base, height, side, and angle.

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Result

Area

40

Perimeter

28

Diagonal 1

12.17

Diagonal 2

7.21

Formulas A = 8 × 5 = 40
P = 2(8 + 6) = 28
d₁ = √(b² + s² + 2bs·cos θ) = 12.17
d₂ = √(b² + s² − 2bs·cos θ) = 7.21

Also in General

Geometry

Parallelogram area, perimeter, diagonals, and angles

The parallelogram area calculator finds the area, perimeter, diagonal lengths, and supplementary angles of a parallelogram from its base, height, side length, and included angle.

Parallelogram formulas

A parallelogram has two pairs of parallel sides. Opposite sides are equal and opposite angles are equal. Consecutive angles are supplementary (they add to 180 degrees).

Area = base * height = base * side * sin(angle). Perimeter = 2 * (base + side). Diagonals are found using the law of cosines: d1 = sqrt(a^2 + b^2 - 2ab*cos(angle)), d2 = sqrt(a^2 + b^2 + 2ab*cos(angle)).

A = b * h

Area from base b and perpendicular height h.

d = sqrt(a^2 + b^2 - 2ab*cos(theta))

Diagonal length via the law of cosines.

Special cases

When the angle is 90 degrees, the parallelogram is a rectangle. When all four sides are equal, it is a rhombus. When both conditions hold, it is a square.

Limitations

The included angle must be between 0 and 180 degrees exclusive. The height must not exceed the side length.

Frequently asked questions

How is a parallelogram different from a rectangle?

A rectangle is a special parallelogram where all angles are 90 degrees. In a general parallelogram, angles can be any value as long as opposite angles are equal and consecutive angles sum to 180 degrees.

Do the diagonals of a parallelogram bisect each other?

Yes. The diagonals always bisect each other, but they are not equal in length unless the parallelogram is a rectangle.

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