Trapezoid Calculator
Enter the two parallel sides and the height for the area and median. Add the two slanted legs to get the perimeter too. The trapezoid is drawn to scale — click a value to change it.
Dimensions
Bases and height are required. Legs are optional (for perimeter).
Results
Trapezoid formulas
A trapezoid (trapezium) has one pair of parallel sides, called the bases. Its area is the average of the two bases times the height.
Area · A = ½ (a + b) · h
Median · m = (a + b) / 2
Perimeter · P = a + b + c + d
About the drawing
When you give the legs, the top base is positioned from the left leg so the figure matches your numbers. With no legs, an isosceles trapezoid is shown for reference and the perimeter is left blank.
What it calculates
Area and the median (mid-segment) from the bases and height, plus the perimeter once both legs are supplied.
Calculating a trapezoid
A trapezoid (called a trapezium in British English) is a four-sided shape with exactly one pair of parallel sides. Those parallel sides are the bases; the other two are the legs. Its area depends only on the two bases and the perpendicular height between them — the legs don't affect it. Supply the legs as well and the calculator can also work out the perimeter.
The parts of a trapezoid
- Bases (a and b) — the two parallel sides, usually one longer than the other.
- Height (h) — the perpendicular distance between the bases, not the slanted leg length.
- Legs (c and d) — the two non-parallel sides. They're only needed for the perimeter.
- Median (mid-segment) — the line halfway up, joining the midpoints of the legs. Its length is the average of the two bases.
Worked example
Take a trapezoid with bases a = 14 and b = 8 and height h = 4. If it's isosceles, the slanted legs work out neatly too.
Each base overhangs by (14 − 8) ÷ 2 = 3. The leg is the hypotenuse of a right triangle with that overhang and the height:
Area 44, median 11, perimeter 32. The legs fall on a 3-4-5 right triangle, which is why they come out as a clean 5.
Formulas this calculator uses
Area · A = ½(a + b)·h
Median · m = (a + b) ÷ 2
Perimeter · P = a + b + c + d
Height from area · h = 2A ÷ (a + b)
Frequently asked questions
How do you find the area of a trapezoid?
Add the two parallel sides (the bases), divide by two to get their average, then multiply by the height: A = ½(a + b)·h. For bases of 14 and 8 with a height of 4, that's ½ × 22 × 4 = 44 square units.
What is the median, or mid-segment, of a trapezoid?
It's the segment joining the midpoints of the two legs, running parallel to the bases halfway up. Its length is the average of the bases: m = (a + b) ÷ 2. The area also equals the median times the height.
How do you find the height of a trapezoid from the area?
Rearrange the area formula. Double the area and divide by the sum of the bases: h = 2A ÷ (a + b). With an area of 44 and bases summing to 22, the height is 88 ÷ 22 = 4.
Do the legs affect the area of a trapezoid?
No. The area depends only on the two bases and the perpendicular height. The legs change the perimeter and the overall slant of the shape, but two trapezoids with the same bases and height have the same area regardless of their legs.
What's the difference between a trapezoid and a parallelogram?
A trapezoid has exactly one pair of parallel sides. A parallelogram has two pairs. So every parallelogram could be seen as a special trapezoid, but a general trapezoid has only one pair of bases and unequal sides.
Is it a trapezoid or a trapezium?
They refer to the same shape — one pair of parallel sides — but the names differ by region. "Trapezoid" is standard in the United States, while "trapezium" is used in the United Kingdom and much of the Commonwealth.