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Trapezoid Area Calculator

Calculate trapezoid area from two parallel side lengths and their perpendicular height in eight common units.

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How to use

  1. 1.Enter the lengths of the two parallel bases using the same measurement unit.
  2. 2.Enter the perpendicular height between those bases and select the shared length unit.
  3. 3.Calculate to read the approximate area in the selected square unit and in square meters.

About Trapezoid Area Calculator

Trapezoid Area Calculator finds the area enclosed by a four-sided figure with one pair of parallel sides. Enter the lengths of parallel base A and parallel base B, enter the perpendicular distance between them, and choose millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. All three measurements must use the same selected unit. The result appears in the square of that unit and as a square-meter equivalent.

The formula is A = (a + b)h/2. It adds the two parallel side lengths, divides their sum by two to find the average base length, and multiplies that average by the perpendicular height. The height is not a slanted leg or diagonal; it is the shortest perpendicular separation between the parallel lines. Reversing base A and base B does not change the result. Equal bases reduce to the familiar rectangle or parallelogram area rule A = bh.

A base may be zero, which supports the triangular limiting case, and both zero bases produce zero area. Height must be greater than zero because zero height does not describe a two-dimensional trapezoid for this calculator. Negative lengths are rejected. This convention is stated explicitly instead of silently replacing invalid values or returning a misleading geometric result.

Length factors are squared for the square-meter result. One foot is exactly 0.3048 meter, so one square foot is 0.09290304 square meter rather than 0.3048 square meter. Metric prefixes follow the same dimensional rule: one square kilometer is one million square meters. The stored factors use the international inch, foot, yard, and mile relationships documented by NIST, not the retired U.S. survey foot.

The formula and unit table are treated as product data. OpenStax anchors the standard one-half-height-times-sum formula, Wolfram MathWorld independently cross-checks trapezoid geometry, and the 2026 NIST Handbook 44 tables anchor unit conversions. Eight executable external golden cases cover unequal and equal bases, a zero-base triangular limit, every supported unit family, decimal and scientific notation, and squared conversions. Tests also require exactly eight unique unit keys and values.

Input syntax is strict and locale-neutral. Each field accepts decimal digits, one optional decimal point, an optional leading sign, and optional e/E scientific notation. Surrounding whitespace is ignored. Commas, embedded spaces, typed units, arithmetic expressions, hexadecimal, Infinity, and NaN are rejected. Each raw field has a 100 UTF-16-code-unit budget that reports an error rather than silently truncating the entry.

Nonzero measurements must normalize from 1e-150 through 1e150 in both the selected unit and meters. These limits keep tiny positive inputs from silently becoming zero and large inputs from becoming Infinity during conversion or area calculation. Zero bases are handled separately. A numeric-range failure produces no area, and editing any measurement or changing the unit immediately clears the prior result or error.

JavaScript uses double-precision floating-point arithmetic, so displayed measurements are approximations. Results show at most six significant digits and use an approximation mark instead of implying unsupported precision; the calculation remains unrounded until display. This tool is suitable for education, estimation, layouts, and ordinary planning, but it does not model measurement uncertainty, land-survey boundaries, curved sides, nonparallel quadrilaterals, or certified metrology.

All parsing, conversion, formula evaluation, and formatting happen in the current browser tab. No measurement, unit, or result is uploaded to Lizely. Measure the perpendicular height and use a consistent unit for all three inputs before relying on the result.

Methodology & sources

Parse three independent decimal or e/E notation inputs under 100-code-unit budgets. Bases must be nonnegative and may be zero; perpendicular height must be positive. Normalize every nonzero length from 1e-150 through 1e150 in both the selected unit and meters, then evaluate A = (a + b)h/2 independently in the selected unit and meter scale. Eight fixed unit records cover mm, cm, m, km, in, ft, yd, and mi; area conversion therefore squares each length factor through the formula. Display uses an approximation mark and at most six significant digits while calculations remain unrounded. Eight external golden cases plus formula, unit-table, syntax, zero-policy, exact-input-budget, underflow, overflow, invalid-unit, and formatting tests enforce behavior.

Frequently asked questions

What formula does the calculator use?
It uses A = (a + b)h/2, where a and b are the parallel side lengths and h is their perpendicular separation.
Can I use a slanted side as the height?
No. Height must be measured perpendicular to the two parallel bases. A slanted leg generally gives a different and incorrect area.
Why is the unit squared?
Area has two length dimensions. Inputs in centimeters produce cm², inputs in feet produce ft², and the calculator also shows the equivalent in m².
Are my measurements uploaded?
No. Validation, unit conversion, area calculation, and formatting all run locally in the current browser tab.

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