The Trapezoid Calculator finds area from the two parallel bases and the perpendicular height, and reports the median segment joining the midpoints of the non-parallel sides. The diagram marks which sides are parallel and draws height at right angles to the base lines.
In US usage a trapezoid has one pair of parallel sides. In UK usage the same shape is often called a trapezium. The formulas on this page follow the US trapezoid definition with one pair of parallels.
Calculate a trapezoid from its bases and height
Parallel bases are the two opposite sides that never meet when extended. Height is the perpendicular distance between those base lines, not the length of a leg unless the leg happens to be vertical on the drawing. Enter b1, b2 and h in consistent units to obtain area and median.
Leg lengths can be stored for perimeter when provided, but the reference fixture uses bases 4 and 8 with height 5 for area-focused work. The engine rejects a zero or negative height.
Calculate the area
Area equals the average of the parallel bases times the height. That average is the same value as the median segment length in a trapezoid, which is why median appears as its own output on this page.
A = ((b1 + b2) / 2) * hFor b1 = 4, b2 = 8, h = 5:
A = ((4 + 8) / 2) * 5 = 6 * 5 = 30Calculate the median
The median, or midsegment, connects the midpoints of the two non-parallel sides and is parallel to the bases. Its length is the arithmetic mean of the base lengths regardless of the leg shapes on the ends.
m = (b1 + b2) / 2For bases 4 and 8:
m = (4 + 8) / 2 = 6Solve a trapezoid with bases 4 and 8 and height 5
Substitute the reference bases and height directly. Area and median share the same average of bases before height multiplies area. 1. Median
m = 62. Area
A = 6 * 5 = 30Understand trapezoid versus trapezium
US textbooks define a trapezoid as a quadrilateral with at least one pair of parallel sides. UK texts often call that shape a trapezium and reserve trapezoid for no parallel sides. The formulas here assume exactly the US trapezoid intent with one parallel pair used in the area formula.
Always note which convention a course uses before comparing answers with an international table. The arithmetic on this page follows the parallel-base formula above.
Frequently asked questions
What is the trapezoid area formula?
A = ((b1 + b2) / 2) * h. For bases 4 and 8 and height 5 the area is 30.
What is the median?
The midsegment length m = (b1 + b2) / 2. For bases 4 and 8 the median is 6.
Is a trapezium the same shape?
In UK usage trapezium often means one pair of parallel sides, matching US trapezoid.
Does height connect the bases?
Height is perpendicular distance between the parallel base lines.
Can both pairs of sides be parallel?
Then the figure is a parallelogram and the parallelogram area formula applies.
How do I find perimeter?
Add all four side lengths when each leg is known. Area only needs bases and height.
Which sides are the bases?
The parallel pair. The diagram highlights them.
Summary
Trapezoid Calculator returns the measures named in the sections above, with substituted arithmetic for every formula and a labelled figure drawn to the entered dimensions. Worked numbers on this page match the geometry reference fixtures.