Trapezoid Area Calculator
Area of a trapezoid from two bases and height, in metric and imperial.
What it does
A trapezoid is a four sided figure with one pair of parallel sides, the two bases. Its area averages those bases and multiplies by the gap between them, which also equals the midline segment times height.
The tool above takes both bases with the perpendicular height in centimeters or inches. It returns the area, the bases added, and the midline. The default 8 and 12 with height 5 gives 50 cm2 with midline 10 cm.
The formula sits in standard prealgebra and contemporary mathematics texts as A = 1/2 h(a + b). Worked checks agree: bases 14 and 11 with height 6 give 75 square inches, and 8 with 6 at height 6 give 42 square centimeters.
Trapezoids model real plots, tables, and garden beds where one end runs wider. When both pairs of sides run parallel the figure is a parallelogram, and when all angles are right it is a rectangle; the same averaging idea covers those as special cases.
How to use
- Pick centimeters or inches.
- Type the two parallel sides as bases.
- Type the perpendicular height, not a slanted leg.
- Read area first, bases and midline beside it.
- Check the midline: area divided by height must match it.
- Convert mirrors land on the same area through 6.4516.
Formula
- a, b
- Parallel base lengths in the same units.
- h
- Perpendicular height between the bases.
- m
- Midline, the average of the two bases.
Imperial inputs convert to centimeters first (x 2.54), then divide square centimeters by 6.4516 for square inches, so both systems agree.
Worked example
Example: bases 8 and 12, height 5
Metric defaults: a 8 cm, b 12 cm, h 5 cm.
- Add bases: 8 + 12 = 20 cm.
- Average: 20 / 2 = 10 cm midline.
- Multiply: 10 x 5 = 50 cm2.
- Imperial check: 3.15, 4.72, 1.97 in gives 7.75 in2.
- Convert: 50 / 6.4516 = 7.75, matching.
- Tool shows 50 cm2, 20 cm, 10 cm.
Reference table
| Bases and height | Midline | Area |
|---|---|---|
| 8 and 12, h 5 cm | 10 cm | 50 cm2 |
| 8 and 6, h 6 cm | 7 cm | 42 cm2 |
| 11 and 14, h 6 in | 12.5 in | 75 in2 |
| 10.3 and 13.7, h 5 ft | 12 ft | 60 ft2 |
Limits
- Needs true parallel bases; skewed quads differ.
- Height must be perpendicular, legs do not qualify.
- Straight sides assumed; curved edges need calculus.
- Units must match across all three inputs.
Common mistakes
- Using a slanted leg as the height.
- Averaging a base with the height.
- Mixing cm and inches in one calculation.
- Forgetting to halve the base sum.
- Reporting length units for an area.
Try it yourself
Quick checks. Answers sit tucked under each question.
Bases 11 and 14, height 6?
Midline 12.5 in, area 75 in2.
Bases 8 and 6, height 6?
Midline 7 cm, area 42 cm2.
Midline of 8 and 12?
10 cm, so area is 10 times height.
Questions
What is the trapezoid formula?
(a + b) / 2 times h: average the bases, times perpendicular height.
What is the midline?
The segment joining the leg midpoints; its length is the base average.
Trapezoid or trapezium?
US trapezoid is UK trapezium: one pair of parallel sides either way.
Can height be slanted?
No. Only the perpendicular gap counts; legs overstate it.
Rectangle case?
Equal bases make the average equal each base, so area is base times height.
Do units convert?
Yes. 50 cm2 is 7.75 in2 through 6.4516.