A parallelogram has opposite sides parallel and equal.
About this calculator
A parallelogram has opposite sides parallel and equal. Area equals base times the perpendicular height — the same rule as a rectangle, because you can shear a rectangle into a parallelogram without changing area.
Do not multiply base by the slant side unless that slant happens to be perpendicular. Enter the altitude h dropped straight down to the base. If you also know the slant edge s, the calculator adds perimeter 2(b + s) and the acute corner angle via arcsin(h/s).
Parallelograms model skewed plots, force diagrams, and offset door frames. A rectangle is a parallelogram with right angles; a rhombus has all sides equal. See [[rectangle]] for the 90° case, [[rhombus]] for equal sides, and [[area]] when mixing several shapes on one site plan.
Common uses
- Skewed land plot area from baseline and perpendicular offset
- Geometry worksheet — base 12, height 5
- Perimeter estimate when slant fence length is known
- Shear-transform proofs — compare with matching rectangle area
- Roof parallelogram panel area on a sloped face
Frequently asked questions
Why not use the slant side for area?
Area needs the altitude perpendicular to the base. Multiplying base × slant overcounts unless the slant is already vertical. Height h must meet the base at 90°.
What is the area when base = 12 and height = 5?
Area = 12 × 5 = 60 square units. If slant side s = 6, perimeter = 2(12 + 6) = 36 units.
How is a parallelogram different from a rectangle?
A rectangle has four right angles. A parallelogram only requires parallel opposite sides. Every rectangle is a parallelogram, but not every parallelogram is a rectangle.
What if height is greater than the slant side?
That cannot happen in a valid parallelogram — the altitude to a side never exceeds that side. Re-check which measurement is height versus slant.