Enter both bases, the height, and both legs — get the area and perimeter instantly.
Enter both bases, height, and both legs to see the results
This trapezoid calculator takes five straightforward measurements — the two parallel bases, the perpendicular height between them, and the two slanted legs — and instantly returns the area and perimeter of the shape they describe. A trapezoid has exactly one pair of parallel sides, so unlike a parallelogram, its two bases are generally different lengths, and the two legs connecting them can differ from each other too. Whether you're computing a garden bed's soil coverage, a bridge cross-section's area, or simply verifying a trapezoid area formula for homework, this free tool applies the correct math and shows every step.
A trapezoid (also called a trapezium in some countries) has one pair of parallel sides — the bases — and two non-parallel sides — the legs. Area depends only on the two bases and the perpendicular height (Area = ½ × (base1 + base2) × height), while perimeter sums all four actual side lengths (Perimeter = base1 + base2 + leg1 + leg2). This calculator takes all five values and computes both results at once.
This tool is built for students verifying trapezoid geometry homework, landscapers laying out trapezoidal garden beds or patios, engineers computing trapezoidal channel, beam, or bridge cross-sections, carpenters cutting trapezoid-shaped tabletops or panels, and anyone with a four-sided shape that has just one pair of parallel sides who needs its area and perimeter without deriving the formulas by hand.
Trapezoids show up wherever a shape tapers from one width to another — a table wider at one end, a canal or channel cross-section, or a bridge support that narrows toward the top. Because the area formula averages the two different base lengths rather than using either one alone, and because the two legs are independent values used only for perimeter, getting all five inputs right is essential for an accurate result.
Landscapers and gardeners lay out trapezoidal garden beds, patios, or driveway aprons and calculate the soil, paving, or edging needed. Structural and civil engineers compute the cross-sectional area of trapezoidal channels, culverts, dams, and bridge supports for flow and material calculations. Carpenters and furniture makers build trapezoid-shaped tabletops, desks, and panels that taper from one width to another. Architects use trapezoidal floor plans and window shapes in modern building designs. Teachers and students use it to check trapezoid geometry problems quickly and accurately.
How both bases, height, and both legs combine to produce area and perimeter
Averaging base1 and base2 before multiplying by height gives the same area as an equivalent rectangle of that average width.
The two non-parallel legs determine the total boundary length but do not appear in the area formula at all.
Both bases, both legs, height, and perimeter are linear measurements; area is always expressed in squared units of the same base unit.
From entering dimensions to reading area and perimeter
Type the lengths of the two parallel sides into the Base 1 (b1) and Base 2 (b2) fields.
Type the perpendicular distance between the two bases into the Height (h) field.
Type the lengths of the two non-parallel sides into the Leg 1 (s1) and Leg 2 (s2) fields.
The calculator averages the two bases and multiplies by height for area, then sums all four sides for perimeter.
Review the area and perimeter shown together in the results panel.
Solving a trapezoid with bases 8 and 4, height 5, and legs 5 and 5.5
A trapezoidal garden bed has a wider base of 8 meters, a narrower base of 4 meters, a height of 5 meters, and slanted edges of 5 and 5.5 meters. What area of soil is needed, and how much edging material is required?
Explanation: Notice the area calculation only used the two bases and the height — the two legs (5 m and 5.5 m) were needed solely for the perimeter, showing how the two formulas draw on different subsets of the five inputs.
What each output represents and how they relate
| Property | What It Represents | Unit Type |
|---|---|---|
| Area | Two-dimensional space enclosed between the two bases and their perpendicular height | Squared (e.g. m², cm², ft²) |
| Perimeter | Total distance around all four sides (two bases, two legs) | Linear (same unit as bases/height/legs) |
Reading the results together: area tells you the two-dimensional surface enclosed by the trapezoid, while perimeter tells you the total edge length needed for framing or bordering — the two results draw on different inputs (bases and height for area; all four sides for perimeter) and don't scale together in a fixed ratio.
Typical ranges: both results must be positive; a trapezoid's area is always between what you'd get using its shorter base alone and its longer base alone (as a rectangle of that height), since the average base sits between the two.
Manual verification: add the two bases, divide by 2, multiply by the height to check area; add all four sides together to check perimeter.
Where computing area and perimeter from bases, height, and legs is genuinely useful
Check trapezoid area and perimeter problems step by step.
Compute trapezoidal support or channel cross-sectional area for engineering specs.
Estimate soil, paving, or edging material for a tapering garden layout.
Build trapezoid-shaped desks or tables that widen from one end to the other.
Calculate trapezoidal channel cross-sections for water flow capacity.
Design trapezoidal window openings, roof faces, or floor plan sections.
Cut trapezoid-shaped fabric panels for A-line skirts or tapered garments.
Estimate the material volume of a trapezoidal retaining wall profile.
Compute trapezoidal roadbed or embankment cross-sectional area.
Calculate area for trapezoid shapes used in logos, posters, or mosaics.
Verify trapezoid component dimensions match design tolerances.
Estimate irregular, tapering land parcel area from base and height measurements.
What this trapezoid calculator does well, and where it doesn't apply
How these related shapes compare
| Shape | Parallel Sides | Area Formula | Inputs Needed for Area |
|---|---|---|---|
| Trapezoid | Exactly one pair | ½ × (b1 + b2) × h | Both bases + height |
| Parallelogram | Two pairs | base × height | Base + height |
| Triangle | None (special case of a trapezoid with one base = 0) | ½ × base × height | Base + height |
Summary: This trapezoid calculator gives you an instant, free way to find the area and perimeter of any trapezoid from its two bases, height, and two legs, with the formula shown. Pair it with related tools like the Parallelogram Calculator and Rectangle Calculator for a fuller picture of quadrilateral geometry.
Common questions about trapezoid measurements
Trusted educational references to go deeper on trapezoids
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