About the Trapezoid Calculator
This trapezoid calculator solves a four-sided shape with one pair of parallel sides — called a trapezoid in the US and a trapezium in the UK. Enter the two parallel bases and the height, all four side lengths, or the area and bases, and it returns the area, perimeter, height, midsegment, both legs, both diagonals and the base angles.
Trapezoids show up in real projects all the time: a tapered garden bed, a gable-end wall section, a roof face on a hip roof, a road cutting cross-section, or a retaining wall. Knowing the area tells you how much material or paint you need, and the perimeter tells you how much edging or trim.
With bases and height, or with area and bases, the calculator assumes an isosceles trapezoid (equal legs) to report legs and angles; the area and height are the same for any trapezoid. With all four sides it solves the exact shape, provided those four lengths can form a trapezoid with a and b parallel.
With the default inputs, the area is 32. Change any value above to recalculate instantly.
How to use the trapezoid calculator
- 1Choose what you know: bases and height, all four sides, or area and bases.
- 2Enter the two parallel sides as base a and base b.
- 3Enter the height, the two legs, or the area.
- 4Read the area and the rest of the measurements.
Formula and method
The area of a trapezoid is the average of the two parallel bases times the perpendicular height between them — equivalently the midsegment (the line joining the midpoints of the legs) times the height. The perimeter is the sum of all four sides.
To solve from four sides, the calculator places base a on the x-axis and finds the horizontal offset of the top base, x = (c² − d² + (a − b)²) ÷ (2(a − b)); the height is then √(c² − x²). Diagonals and base angles follow from the corner coordinates. When only bases and height are known, the offset is taken as (a − b) ÷ 2, i.e. an isosceles trapezoid; working from area, h = 2A ÷ (a + b).
- a, b
- Parallel sides (bases)
- c, d
- Non-parallel sides (legs)
- h
- Perpendicular height between the bases
- m
- Midsegment (median)
Worked examples
Bases 10 and 6, height 4
A = ½ × (10 + 6) × 4 = 32. As an isosceles trapezoid each leg overhangs by 2, so the legs are √(4² + 2²) ≈ 4.47 and the perimeter is about 24.94.
Four sides: bases 12 and 7, legs 5 and 6
The top base is offset by x = (25 − 36 + 25) ÷ 10 = 1.4, so h = √(25 − 1.96) = 4.8. The area is ½ × 19 × 4.8 = 45.6, and the base angles are about 73.74° and 53.13°.
Garden bed: area 50 sq ft with 12 ft and 8 ft sides
h = 2 × 50 ÷ (12 + 8) = 5 ft. If the bed is symmetrical, each sloping side is √(5² + 2²) ≈ 5.39 ft, so you need about 30.8 ft of edging.
Frequently asked questions
What is the formula for the area of a trapezoid?+
A = ½ × (a + b) × h: add the two parallel sides, halve the sum, and multiply by the perpendicular height. Bases 10 and 6 with height 4 give 32.
Is a trapezoid the same as a trapezium?+
Yes, in modern usage. “Trapezoid” is the US term and “trapezium” the UK and Commonwealth term for a quadrilateral with one pair of parallel sides.
How do I find the height of a trapezoid?+
If you know the area, h = 2A ÷ (a + b). If you know all four sides, use the offset x = (c² − d² + (a − b)²) ÷ (2(a − b)) and then h = √(c² − x²).
What is the midsegment of a trapezoid?+
It is the segment joining the midpoints of the two legs. It is parallel to the bases and its length is their average, (a + b) ÷ 2, so area also equals midsegment × height.
Can I use the slanted side as the height?+
No. The height must be measured perpendicular to the bases. Using the slanted leg overstates the area unless the trapezoid has a right angle on that side.