Parallelogram Calculator
Calculate parallelogram area, perimeter, base, height, and side lengths with step-by-step geometric formulas.
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What Is a Parallelogram Calculator?
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. Opposite interior angles are equal, and consecutive angles are supplementary (sum to 180°).
How to Use This Calculator
- Enter the base (b), height (h), and slant side (a).
- View the calculated Area and Perimeter.
- Follow the step-by-step calculations.
Parallelogram Area and Perimeter Formulas
A = b \times h, \quad P = 2(a + b)Area is the product of the base and perpendicular height. Perimeter is twice the sum of adjacent sides a and b.
Worked Example
Scenario: Find area and perimeter for base b = 15 cm, height h = 8 cm, side a = 10 cm
Area: A = b × h = 15 × 8 = 120 cm²
Perimeter: P = 2 × (10 + 15) = 2 × 25 = 50 cm
Tips & Key Notes
- Height must be measured perpendicular to the base, not along the slanted side.
- If the interior angles are 90°, the parallelogram is a rectangle.
- Diagonals of a parallelogram bisect each other.
Frequently Asked Questions
What is the difference between slant side and height?
The slant side is the actual edge of the shape, while height is the perpendicular (shortest) distance between parallel sides.
Can you calculate area from sides and angle?
Yes, Area = a × b × sin(θ), where θ is the angle between sides a and b.
Do diagonals bisect each other in a parallelogram?
Yes, the two diagonals cross at their exact midpoints, though they are not generally equal in length.
What shapes are parallelograms?
Squares, rectangles, and rhombuses are all special types of parallelograms.
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