Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a trapezoid's area from its two parallel bases and height.
25.0000
This tool calculates the area of a trapezoid (a quadrilateral with one pair of parallel sides) from its two base lengths and the height between them.
Enter both parallel base lengths and the height. The area appears instantly.
Area = ((base1 + base2) / 2) × height
The formula averages the two parallel sides and then multiplies by the height. This is equivalent to imagining a rectangle whose width is the midpoint of the two bases; the extra triangle of area on the long side is exactly balanced by the missing triangle on the short side. Another way to see it is to place two identical trapezoids together, one flipped, to form a parallelogram with base equal to base 1 plus base 2 and the same height. The trapezoid is half of that parallelogram, hence the division by two.
Suppose a hypothetical garden bed is shaped like a trapezoid. The wide edge along the fence is 9.5 meters, the narrow edge at the front is 6 meters, and the perpendicular distance between them is 4 meters. Enter base 1 = 9.5, base 2 = 6, and height = 4.
Area = ((9.5 + 6) / 2) × 4 = 7.75 × 4 = 31 square meters
The bed covers 31 square meters. Multiply by a planned depth to estimate soil volume, or by a coverage rate to estimate seed or mulch, following the product packaging.
The height is the single most common source of errors. It is the perpendicular distance between the two parallel bases, measured at a right angle. The slanted sides are always longer than the height unless the trapezoid is a right trapezoid, where one slanted side is itself perpendicular. If you only know the slanted length and an angle, you can find the height with trigonometry: height = slanted side × sin(angle between the slanted side and the base). If you know all four sides but no height, additional geometry is needed; this tool takes the height directly.
Only the two parallel sides are bases. Before entering values, identify which pair of sides is parallel. It does not matter which base is entered first, since the formula adds them. If the trapezoid is oriented with the bases vertical rather than horizontal, the "height" is the horizontal distance between them.
Trapezoids appear in roof planes, sloped garden beds, road cross-sections, drainage channels, tabletops, and some plots of land. For irregular lots, dividing the shape into trapezoids and triangles and adding their areas is a common survey technique. The answer describes ideal geometry, so for buying materials, round up and allow for waste.
The perpendicular distance between the two parallel bases -- not the length of a slanted side.
No. The formula adds the two bases together, so swapping them gives the same area.
Only in a right trapezoid. In other trapezoids the slanted side is longer than the perpendicular height, and using it will overstate the area.
Then the shape is a parallelogram, and the result equals base times height. The calculator handles this case correctly.
Square units of whatever you entered. Bases and height in meters give an area in square meters.
Reference: NIST Weights and Measures