Trapezoid Area: worked example
| Top base | 10 |
|---|---|
| Bottom base | 6 |
| Height | 4 |
| Area | 32 |
| Midsegment length | 8 |
Trapezoid Area: formula
Enter the lengths of the two parallel sides, the bases, and the perpendicular height between them. The height is the shortest distance between the bases, not the slanted side. The area is the average of the bases times the height, and the midsegment is the average of the bases.
Use the same unit for all three, and check that the two bases are truly parallel.
Trapezoid Area: changing Top base
| Top base | Area | Midsegment length |
|---|---|---|
| 8 | 28 | 7 |
| 9 | 30 | 7.5 |
| 10 (example) | 32 | 8 |
| 11 | 34 | 8.5 |
| 12 | 36 | 9 |
Trapezoid Area: compare input ranges
| Input | Tested from | To | Area: low input | Area: high input | Swing |
|---|---|---|---|---|---|
| Height | 3.6 | 4.4 | 28.8 | 35.2 | 6.4 (20%) |
| Top base | 9 | 11 | 30 | 34 | 4 (13%) |
| Bottom base | 5.4 | 6.6 | 30.8 | 33.2 | 2.4 (7.5%) |
Trapezoid Area: individual input comparisons
| Input | Value | Area | Midsegment length |
|---|---|---|---|
| Top base | 8 | 28 | 7 |
| 9 | 30 | 7.5 | |
| 10 | 32 | 8 | |
| 11 | 34 | 8.5 | |
| 12 | 36 | 9 | |
| Bottom base | 4.8 | 29.6 | 7.4 |
| 5.4 | 30.8 | 7.7 | |
| 6 | 32 | 8 | |
| 6.6 | 33.2 | 8.3 | |
| 7.2 | 34.4 | 8.6 | |
| Height | 3.2 | 25.6 | 8 |
| 3.6 | 28.8 | 8 | |
| 4 | 32 | 8 | |
| 4.4 | 35.2 | 8 | |
| 4.8 | 38.4 | 8 |
Trapezoid Area: combined input changes
| Top base / Bottom base | 4.8 | 6 | 7.2 |
|---|---|---|---|
| 8 | 25.6 | 28 | 30.4 |
| 9 | 27.6 | 30 | 32.4 |
| 10 | 29.6 | 32 | 34.4 |
| 11 | 31.6 | 34 | 36.4 |
| 12 | 33.6 | 36 | 38.4 |
Trapezoid Area: which assumptions move the result?
Trapezoid Area: values and definitions
| Quantity and definition | Value used |
|---|---|
| Top base — One of the two parallel sides. | 10 |
| Bottom base — The other parallel side. | 6 |
| Height — The perpendicular distance between the two bases, not the slanted side. | 4 |
| Area | 32 |
| Midsegment length | 8 |
Trapezoid Area: half and double Height
| Height | Area |
|---|---|
| 2 | 16 |
| 4 | 32 |
| 8 | 64 |
Common error: Averaging all four sides. Only the two parallel bases go into the average; the slanted legs never appear in the area.
The slanted legs do not enter the area formula, only the perpendicular height, so measuring the leg instead of the height gives the wrong answer. Some definitions require exactly one pair of parallel sides. For shapes with curved sides, the result is an approximation.
Geometry calculators: Parallelogram Area Calculator, Rectangular Prism Volume Calculator, Triangle Third Side Calculator, Arc Length and Sector Area Calculator, Ellipse Area Calculator, Pyramid Volume Calculator.
A trapezoid's area is the average of its two parallel sides times the distance between them. Average first, multiply second. A lot 10 feet wide at the street and 6 feet at the back, 4 feet deep, covers 32 square feet, the same as a rectangle 8 feet wide.
The midsegment output is that 8. It is the width you could use to pretend the shape is a plain rectangle.
Measure the height at right angles to the parallel sides. Laying the tape along the slanted edge gives a longer number and a larger, wrong area.
See the parallelogram, rectangle and triangle calculators for related shapes, and the rhombus page for another quadrilateral. The land acreage and unit conversion calculators turn the result into acres or square meters, and the concrete and paving tools estimate materials for such areas.
What is the formula for the area of a trapezoid?
Half the sum of the parallel sides times the height. Bases 10 and 6 with height 4 give 32.
Which height do I use?
The perpendicular distance between the two parallel sides, not the length of the slanted sides, which are always longer than the height unless the shape is a rectangle.
What is the midsegment of a trapezoid?
The segment joining the midpoints of the legs, parallel to the bases, with a length equal to their average.