Parallelogram Calculator
Calculate parallelogram area, perimeter, diagonals, angles, and height. Enter sides and angles to get all measurements with interactive visualization.
A = base x height | P = 2(a + b)Parallelogram Properties
Area
60.6218 cm^2
Parallelogram Input
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Complete Results
Sides
Side a
10.0000 cm
Side b
7.0000 cm
Angles
Angle A (and C)
60.00deg
Angle B (and D)
120.00deg
Measurements
Area
60.6218 cm^2
A = base x height
Perimeter
34.0000 cm
P = 2(a + b)
Height
6.0622 cm
h = b x sin(A)
Diagonals
Diagonal 1
8.8882 cm
Diagonal 2
14.7986 cm
Check: d1^2 + d2^2 = 298.0000, 2(a^2 + b^2) = 298.0000
Parallelogram Formulas
Area Formulas
- A = base x height
- A = a x b x sin(angle)
- A = (1/2) x d1 x d2 x sin(theta)
Diagonal Formulas
- d1 = sqrt(a^2+b^2-2ab cos A)
- d2 = sqrt(a^2+b^2+2ab cos A)
- d1^2 + d2^2 = 2(a^2+b^2)
Tip: Consecutive angles in a parallelogram always sum to 180 degrees. If you know one angle, the adjacent angle is 180 degrees minus that angle.
Special Cases
Rectangle
All angles = 90 degrees. Diagonals are equal.
Rhombus
All sides equal. Diagonals perpendicular.
Square
Rectangle + Rhombus. All sides equal, all angles 90 degrees.
Parallelogram Properties
Area
60.6218 cm^2
?How to Calculate Parallelogram Properties
Parallelogram formulas: Area = base x height = a x b x sin(angle). Perimeter = 2(a + b). The diagonals bisect each other. Opposite angles are equal and consecutive angles are supplementary (sum to 180 degrees). Both diagonals can be calculated using the law of cosines.
What is a Parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, opposite angles are equal, and consecutive angles are supplementary (add up to 180 degrees). The diagonals of a parallelogram bisect each other. Special cases include rectangles (with right angles), rhombi (with equal sides), and squares (with both).
Key Facts About Parallelograms
- Area = base x height = a x h
- Area = a x b x sin(angle) using sides and included angle
- Perimeter = 2(a + b) = 2a + 2b
- Opposite sides are equal and parallel
- Opposite angles are equal
- Consecutive angles are supplementary (sum to 180 degrees)
- Diagonals bisect each other (but are not equal unless rectangle)
- d1^2 + d2^2 = 2(a^2 + b^2) - parallelogram law
- A rectangle is a special parallelogram with 90 degree angles
- A rhombus is a special parallelogram with all sides equal
Quick Answer
Parallelogram formulas: Area = base x height = a x b x sin(angle). Perimeter = 2(a + b). The diagonals bisect each other. Opposite angles are equal and consecutive angles are supplementary (sum to 180 degrees). Both diagonals can be calculated using the law of cosines.
Parallelogram Practice Problems
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Practice with 4 problems to test your understanding.
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Frequently Asked Questions
The area of a parallelogram can be calculated as: Area = base x height, or Area = a x b x sin(angle), where a and b are adjacent sides and angle is the included angle between them.
Using the law of cosines: d1 = sqrt(a^2 + b^2 - 2ab cos(A)) and d2 = sqrt(a^2 + b^2 + 2ab cos(A)), where A is one of the angles. The diagonals bisect each other but are generally not equal.
Opposite angles are equal (angle A = angle C, angle B = angle D). Consecutive angles are supplementary, meaning they add up to 180 degrees (angle A + angle B = 180).
A parallelogram is a rectangle when all four angles are right angles (90 degrees). In this case, the diagonals are equal in length.
A parallelogram is a rhombus when all four sides are equal in length. In a rhombus, the diagonals bisect each other at right angles.
The parallelogram law states that the sum of the squares of the diagonals equals twice the sum of the squares of the sides: d1^2 + d2^2 = 2(a^2 + b^2).
Last updated: 2025-01-15
Parallelogram Properties
Area
60.6218 cm^2