Parallelogram Area: worked example
| Base | 8 |
|---|---|
| Perpendicular height | 5 |
| Slanted side | 6 |
| Area | 40 |
| Perimeter | 28 |
Parallelogram Area: formula
Measure the perpendicular separation of the parallel bases for height. The slanted side is a different measurement used for the boundary length. Keep all three entries in the same unit; a slanted side cannot be shorter than the perpendicular height for this geometry.
Parallelogram Area: changing Base
| Base | Area | Perimeter |
|---|---|---|
| 6 | 30 | 24 |
| 7 | 35 | 26 |
| 8 (example) | 40 | 28 |
| 9 | 45 | 30 |
| 10 | 50 | 32 |
Parallelogram Area: compare input ranges
| Input | Tested from | To | Area: low input | Area: high input | Swing |
|---|---|---|---|---|---|
| Base | 7 | 9 | 35 | 45 | 10 (25%) |
| Perpendicular height | 4.5 | 5.5 | 36 | 44 | 8 (20%) |
| Slanted side | 5.4 | 6.6 | 40 | 40 | 0 |
Parallelogram Area: individual input comparisons
| Input | Value | Area | Perimeter |
|---|---|---|---|
| Base | 6 | 30 | 24 |
| 7 | 35 | 26 | |
| 8 | 40 | 28 | |
| 9 | 45 | 30 | |
| 10 | 50 | 32 | |
| Perpendicular height | 4 | 32 | 28 |
| 4.5 | 36 | 28 | |
| 5 | 40 | 28 | |
| 5.5 | 44 | 28 | |
| 6 | 48 | 28 | |
| Slanted side | 4.8 | 40 | 25.6 |
| 5.4 | 40 | 26.8 | |
| 6 | 40 | 28 | |
| 6.6 | 40 | 29.2 | |
| 7.2 | 40 | 30.4 |
Parallelogram Area: combined input changes
| Base / Perpendicular height | 4 | 5 | 6 |
|---|---|---|---|
| 6 | 24 | 30 | 36 |
| 7 | 28 | 35 | 42 |
| 8 | 32 | 40 | 48 |
| 9 | 36 | 45 | 54 |
| 10 | 40 | 50 | 60 |
Parallelogram Area: which assumptions move the result?
Parallelogram Area: values and definitions
| Quantity and definition | Value used |
|---|---|
| Base — The length of the side you measure the height from. | 8 |
| Perpendicular height — The straight-up distance to the opposite side, not the slanted side. | 5 |
| Slanted side — The length of the slanted side, used only for the perimeter. | 6 |
| Area | 40 |
| Perimeter | 28 |
Parallelogram Area: half and double Base
| Base | Area |
|---|---|
| 4 | 20 |
| 8 | 40 |
| 16 | 80 |
Common error: Multiplying the base by the slanted side. That gives an area larger than the real one, and the error grows the more the shape leans.
Confusing the height with the side is the most common error. The perimeter uses the side length while the area uses the height. A rhombus is a parallelogram with equal sides, and a rectangle is a parallelogram with right angles.
Units must match.
Geometry calculators: Rectangular Prism Volume Calculator, Triangle Third Side Calculator, Arc Length and Sector Area Calculator, Ellipse Area Calculator, Pyramid Volume Calculator, Right Triangle & Pythagorean Calculator.
Slide the slanted end of a parallelogram over and it becomes a rectangle with the same base and height, which is why the area is just base times height. The slant only affects the perimeter. With a base of 8 and a height of 5 the area is 40 whether the side leans a little or a lot, but the perimeter grows as the side gets longer.
Confirm the height is the straight-up distance to the opposite side. If you measured along the lean, that number belongs in the side field instead.
See the rectangle, trapezoid and rhombus calculators for related shapes, the triangle area page since a parallelogram splits into two triangles, and the trigonometry calculator for finding heights from angles. The land acreage and unit conversion pages change units.
Why is the height not the slanted side?
Because area depends on the perpendicular distance between the parallel sides, and the slanted side is longer than that distance.
What is the area of a parallelogram?
The base times the perpendicular height. A base of 8 and height of 5 give 40.
How is a parallelogram related to a rectangle?
Cutting the slanted end and moving it to the other side turns the parallelogram into a rectangle with the same base and height.