A parallelogram’s area, computed simply as base times perpendicular height — no halving needed, unlike a triangle.
How it works
Multiplying the base by the perpendicular height gives the area; if a slanted side length is also given, doubling the sum of the base and that side gives the perimeter.
What this does not include
This does not include other shapes — for a multi-shape tool covering rectangles, circles, trapezoids and more, use this site’s general area calculator instead.
How to use this calculator
- Enter the base and perpendicular height; add the slanted side length for the perimeter.
A worked example
A parallelogram with base 10, height 6: area = base × height = 60.
Base 8, height 5, side 6: area = 40, perimeter = 2(8+6) = 28.
What the variables mean
| Variable | Meaning |
|---|---|
| Base | Length of the base side |
| Height | Perpendicular distance between the base and its opposite side |
| Side | Length of an adjacent (slanted) side, only needed for perimeter |
Edge cases worth knowing
Height is the perpendicular distance, not the slanted side length. A common mistake is using the slant side in place of height — area needs the true perpendicular measurement, which is usually shorter than the slant.
A base of zero collapses the parallelogram to a line, so the calculator declines to show a result.
Frequently asked questions
What does “perpendicular height” mean?
The straight-up distance between the base and the opposite side, at a right angle — not the length of the slanted side itself, which would overstate the area if used instead.
Why doesn’t a parallelogram’s area formula need dividing by 2, unlike a triangle?
A parallelogram is a full base-by-height rectangle sheared sideways — no area is lost in that shearing, unlike a triangle, which is exactly half of the same base-by-height rectangle.
Is a rectangle a special case of a parallelogram?
Yes — a rectangle is a parallelogram where all angles happen to be 90 degrees, and this same area formula applies unchanged.
