Parallelogram Area Calculator
Calculate the area of a parallelogram using base and height, sides and angle, or diagonals and angle
Calculate Parallelogram Area
Length of the base of the parallelogram
Perpendicular distance between parallel sides
Calculation Results
Formula used: Area = base × height
Example Calculations
Base and Height Method
Given: Base = 8 cm, Height = 5 cm
Formula: Area = base × height
Calculation: Area = 8 × 5 = 40 cm²
Sides and Angle Method
Given: Side A = 5 cm, Side B = 13 cm, Angle = 30°
Formula: Area = a × b × sin(angle)
Calculation: Area = 5 × 13 × sin(30°) = 5 × 13 × 0.5 = 32.5 cm²
Diagonals and Angle Method
Given: Diagonal 1 = 10 cm, Diagonal 2 = 15 cm, Angle = 90°
Formula: Area = ½ × e × f × sin(angle)
Calculation: Area = ½ × 10 × 15 × sin(90°) = ½ × 10 × 15 × 1 = 75 cm²
Parallelogram Properties
Opposite sides are parallel and equal
Opposite angles are equal
Adjacent angles are supplementary (sum to 180°)
Diagonals bisect each other
Sum of all angles is 360°
Area Formulas
Base × Height
A = b × h
Sides × Angle
A = a × b × sin(θ)
Diagonals × Angle
A = ½ × e × f × sin(φ)
Calculation Tips
Height is always perpendicular to the base
Any side can be used as the base
Adjacent angles are supplementary
sin(θ) = sin(180° - θ) for any angle
Understanding Parallelogram Area Calculation
What is a Parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. This includes rectangles, rhombuses, and squares as special cases. The area represents the amount of space enclosed within the parallelogram's boundaries.
Key Characteristics
- •Opposite sides are parallel and equal in length
- •Opposite angles are equal
- •Adjacent angles are supplementary (sum to 180°)
- •Diagonals bisect each other but are not necessarily equal
Calculation Methods
Base and Height
Most straightforward method
Area = base × height
Sides and Angle
Uses trigonometry
Area = a × b × sin(θ)
Diagonals and Angle
When diagonals are known
Area = ½ × e × f × sin(φ)
Note: All methods give the same result for the same parallelogram. Choose the method based on which measurements you have available.