Key takeaways
- The area of a parallelogram is A = base × height.
- Height must be perpendicular to the base, never the length of the slanted side.
- Shearing a rectangle into a parallelogram keeps the area the same, as long as base and height don't change.
- A parallelogram has two pairs of parallel sides; a trapezoid has only one.
In this guide
What is a parallelogram?
A parallelogram has two pairs of parallel sides, but unlike a rectangle, its corners aren't necessarily right angles. Think of a rectangle that's been pushed sideways.
Why does the area of a parallelogram matter?
Parallelograms show up in slanted roofs, banners, and land plots, and their area follows the exact same rule as a rectangle: base times height.
Take a 10 m × 6 m rectangle (area 60 m²) and push its top sideways into a parallelogram, keeping the same 10 m base and 6 m perpendicular height. The area is still exactly 60 m², even though the slanted sides are now longer than 6 m.
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 60 m² |
| base | The length of one side, usually the bottom | 10 m |
| height | The perpendicular distance to the opposite side | 6 m |
How to find the area step by step
- 1Measure the base. The length of one side.
- 2Measure the height. The straight up-and-down distance to the opposite parallel side, not the slanted side.
- 3Multiply base by height.
- 4Add square units. Such as m² or ft².
Now try it yourself. Change the base and height in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Confusing this with a [trapezoid](/calculator/area-trapezoid). A trapezoid has only one pair of parallel sides; a parallelogram has two.
- Forgetting square units. Area is always in units², like m² or ft².
- Assuming a bigger-looking shape has more area. A more slanted parallelogram can look bigger while covering the exact same area, if base and height are unchanged.
Tips and tricks
- If all four sides happen to be equal, you're really looking at a rhombus, which can also be found from its diagonals.
- If the two pairs of sides aren't parallel at all, you likely need Heron's formula or a different approach entirely.
Where you'll use it in real life
- Roofing: sizing a slanted roof panel.
- Textiles: calculating fabric for a parallelogram-shaped banner.
- Land surveying: working out area for an oddly shaped plot of land.
- Architecture: estimating material for slanted wall sections.
Quick summary
To find the area of a parallelogram, multiply the base by the perpendicular height, never the slanted side. Shearing a rectangle into a parallelogram doesn't change its area, as long as base and height stay fixed. Use the calculator above to check your own shape instantly.
Worked example
A slanted greenhouse roof panel is shaped like a parallelogram with a base of 10 meters and a perpendicular height of 6 meters. How much roofing material do you need?
- 01A = base × height
- 02A = 10 × 6
- 03A = 60 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How is a parallelogram's area formula different from a rectangle's?
They're the same formula (base × height), but for a parallelogram the height must be measured perpendicular to the base, since the sides are slanted rather than at 90°.
What's the difference between a parallelogram and a rhombus?
A rhombus is a special parallelogram where all four sides are equal length. Its area can also be found from its diagonals using the [rhombus area calculator](/calculator/area-rhombus).
Can I use the side length instead of the height?
No, the slanted side is longer than the perpendicular height, so using it directly would overstate the area. You need the true perpendicular height.
How is a parallelogram different from a trapezoid?
A parallelogram has two pairs of parallel sides. A [trapezoid](/calculator/area-trapezoid) has only one pair, so it uses a different area formula.
