Parallelogram Perimeter Calculator
Calculate parallelogram perimeter using sides, diagonals, or base with height and angle
Calculate Parallelogram Perimeter
Length of the first side
Length of the adjacent side
Calculation Results
Formula used: Perimeter = 2 × (a + b)
Example Calculations
Two Sides Method
Given: Side A = 8 cm, Side B = 6 cm
Formula: Perimeter = 2 × (a + b)
Calculation: Perimeter = 2 × (8 + 6) = 28 cm
Side and Diagonals Method
Given: Side = 15 in, Diagonal 1 = 18 in, Diagonal 2 = 24 in
Formula: P = 2 × (a + √((e² + f² - 2a²) / 2))
Other side: √((18² + 24² - 2×15²) / 2) = √((324 + 576 - 450) / 2) = √225 = 15 in
Perimeter: 2 × (15 + 15) = 60 in
Base, Height, and Angle Method
Given: Base = 10 cm, Height = 6 cm, Angle = 60°
Formula: Perimeter = 2 × (a + h/sin(angle))
Adjacent side: 6/sin(60°) = 6/0.866 ≈ 6.93 cm
Perimeter: 2 × (10 + 6.93) = 33.86 cm
Parallelogram Properties
Opposite sides are parallel and equal
Opposite angles are equal
Adjacent angles are supplementary
Diagonals bisect each other
Perimeter = 2 × (sum of adjacent sides)
Perimeter Formulas
Two Sides
P = 2(a + b)
Side + Diagonals
P = 2a + √(2e² + 2f² - 4a²)
Base + Height + Angle
P = 2(a + h/sin(θ))
Calculation Tips
Simplest method is with two adjacent sides
Diagonal method uses parallelogram law
Adjacent angles are supplementary
Check diagonal constraints for validity
Understanding Parallelogram Perimeter Calculation
What is Perimeter?
The perimeter of a parallelogram is the total length of its boundary, calculated by adding the lengths of all four sides. Since opposite sides are equal in a parallelogram, the perimeter is simply twice the sum of two adjacent sides.
Parallelogram Law
The parallelogram law states that for any parallelogram with sides a and b, and diagonals e and f:
2a² + 2b² = e² + f²
This relationship allows us to find unknown sides when diagonals are known.
Calculation Methods
Two Sides
Most direct method
P = 2(a + b)
Side and Diagonals
Uses parallelogram law
P = 2a + √(2e² + 2f² - 4a²)
Base, Height, Angle
Uses trigonometry
P = 2(a + h/sin(θ))
Note: For the diagonal method, the values must satisfy geometric constraints to form a valid parallelogram.