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How to use
Use the trapezoid calculator to find area, perimeter, height, a missing base or the midsegment. Area depends on the two parallel bases and perpendicular height, while perimeter also requires the two leg lengths. The area formula is A = (a + b) × h ÷ 2. Reverse it with h = 2A ÷ (a + b), or find a missing base using b = 2A ÷ h − a. The recovered base must be positive. Trapezium is the UK name for the same two-parallel-base shape described here.
- Choose direct calculation or an inverse height/base mode.
- Enter known values in one consistent unit.
- In direct mode, optionally add both legs for perimeter.
- Calculate and review area, midsegment and solved measurements.
How it is calculated
Example
Bases 8 and 12 with height 5 give area 50 and midsegment 10. If area 50 and those same bases are entered in inverse mode, height 5 is recovered.
Important notes
Height is the perpendicular distance between the bases, not a slanted leg. Perimeter requires the actual leg lengths; the tool never silently assumes an isosceles trapezoid.
Worked examples and interpreting results
A trapezoid with parallel bases 10 and 6 and perpendicular height 4 has area 32 square units. Multiply the average of the bases by height, rather than by a sloping side.
| Case | Calculation | Result |
|---|---|---|
| Area from bases and height | (10 + 6) × 4 ÷ 2 | 32 |
| Recover height from area | 2 × 32 ÷ (10 + 6) | 4 |
How to check the result
In general, the bases and height do not determine the perimeter. You also need both non-parallel side lengths or additional geometric information. Keep all lengths in the same unit.
Trapezoid area, inverse height and perimeter
The area of a trapezoid is half the sum of its parallel bases multiplied by perpendicular height. If area and both bases are known, solve for height with 2 × area ÷ (base 1 + base 2). The midsegment is the average of the bases.
- Area from bases 9 and 5, height 4: (9 + 5) × 4 ÷ 2 = 28
- Height from area 42 and bases 8 and 6: (2 × 42) ÷ (8 + 6) = 6
- Perimeter with bases 8 and 14, legs 5 and 5: 8 + 14 + 5 + 5 = 32
Important distinction
A slanted leg is not the perpendicular height. To calculate perimeter, both nonparallel side lengths are also required; bases and height alone do not determine it.
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Frequently asked questions
How do I calculate the area of a trapezoid?
Add the parallel bases, multiply by the perpendicular height and divide by 2: A = (a + b)h/2. Bases of 8 cm and 12 cm with height 5 cm give 50 cm².
How do I find trapezoid height from area?
Use h = 2A/(a + b). With area 50 cm² and bases 8 cm and 12 cm, height is 5 cm. Select the inverse height mode and enter those known values.
Are bases and height enough for perimeter?
No. They determine area, not the two leg lengths.
What is the midsegment?
It is the average of the two bases: (a+b)/2.
Can a base be solved from area?
Yes, when area, height and the other base are known.
What is the area of a trapezoid with bases 8 and 12 and height 5?
The area of a trapezoid is A = (a + b)h/2, where a and b are the parallel bases and h is their perpendicular separation. For bases 8 and 12 and height 5, area = (8 + 12) × 5/2 = 50 square units.
Can a trapezoid's perimeter be found from bases and height alone?
Not for a general trapezoid. You need the two nonparallel leg lengths as well: perimeter = a + b + c + d. The same two bases and height can produce different side lengths, so do not assume it is isosceles.