Parallelogram Formulas
Perimeter = 2 × (base + side)
Height = Area / base
Area (with angle) = base × side × sin(θ)
The height is the perpendicular distance between the two parallel bases — not the slant side length.
Example
Parallelogram: base = 10 cm, height = 6 cm, side = 7 cm
Area = 10 × 6 = 60 cm²
Perimeter = 2 × (10 + 7) = 34 cm
Parallelogram vs Rectangle
| Property | Rectangle | Parallelogram |
|---|---|---|
| Opposite sides | Equal & parallel | Equal & parallel |
| Angles | All 90° | Opposite angles equal |
| Diagonals | Equal length, bisect each other | Bisect each other, not equal |
| Area formula | length × width | base × height |
Frequently Asked Questions
Is a rectangle a parallelogram?
Yes — a rectangle is a special case of a parallelogram where all angles are 90°. A square is a special rectangle (and parallelogram) where all sides are equal. So all rectangles are parallelograms, but not all parallelograms are rectangles.
What is the difference between height and side in a parallelogram?
The side (leg) is the slant length of the non-base edges. The height is the perpendicular (straight-down) distance between the two parallel bases. The area formula uses height, not side length. If you only know the side and angle, use: Area = base × side × sin(θ).
What are real-world examples of parallelograms?
Slanted floor tiles, some table tops, parallelogram-shaped road signs, the cross-section of a slanted cut through a prism, and many structural components in engineering and architecture.