Last updated: 2026-05-18

What a parallelogram is

A parallelogram is a four-sided figure with two pairs of parallel sides. Its area depends on the base and the perpendicular height — the vertical distance between the base and the opposite side, not the slant length. This calculator applies the formula A = b × h and returns the result.

Formula

where $b$ is the length of the base and $h$ is the perpendicular height (altitude). The height is measured at a 90° angle to the base, regardless of how much the parallelogram leans.

Worked example

A parallelogram has a base of 8 cm and a perpendicular height of 5 cm.

Shearing the parallelogram upright into a rectangle preserves both the base and the height, and therefore the area. This is why the formula is identical to the rectangle formula.

Perpendicular height vs. slant side

The area formula uses the perpendicular height, not the slant side length. The slant side is always longer than the perpendicular height, except when the angle is exactly 90°, in which case the figure is a rectangle and the two lengths coincide.

If you know the slant side $s$ and the interior angle $\theta$ between the base and the slant side, the perpendicular height is:

Substitute this into the area formula to get $A = b \times s \times \sin(\theta)$.

Related shapes