Trapezoid Area Calculator Guide

What This Calculator Does

The Trapezoid Area Calculator takes two parallel bases and the perpendicular height. It gives the area in the square of your chosen length unit, plus square metres and square feet. A labelled schematic identifies a, b and h; the drawing does not scale to the entered measurements.

When to Use It

Use it for a geometry problem or a flat region measured as a trapezoid. For triangles use the triangle calculator; for combined regions use square footage. A slanted side alone is not enough to determine height.

Inputs Explained

Both bases and height must be positive. Choose metres, centimetres, millimetres, feet or inches. Changing the unit converts valid dimensions to preserve their physical size. Enter plain decimals or scientific notation, without units, expressions or thousands separators.

Confirm that the two entered bases are parallel, then measure height perpendicular to them. Leaning the trapezoid left or right does not change its area when bases and height stay the same. If a diagram labels only a slanted side, determine perpendicular height separately before using this tool.

For example, 80 cm, 120 cm and 50 cm produce 5000 cm², or 0.5 m². This equals the result from 0.8 m, 1.2 m and 0.5 m. Entering centimetre values while metres are selected would multiply the area by ten thousand.

How the Calculation Works

$$A=\frac{a+b}{2}h$$

Average the lengths of the parallel bases and multiply by the perpendicular height. Internally dimensions are converted to metres. The selected square unit uses the length factor squared: 1 ft²=0.09290304 m² because 1 ft=0.3048 m.

Two identical trapezoids can be rotated and joined into a parallelogram with base a+b and height h. Its area is (a+b)×h, and each original trapezoid is half of it. This explains the division by two without requiring equal slanted sides or symmetry; the calculator does not assume an isosceles trapezoid.

Example

Bases 8 m and 12 m with height 5 m give (8+12)/2×5=50 m², approximately 538.195521 ft². Two equal 10 m bases give the same area. Equal bases are accepted, regardless of whether your textbook uses an inclusive or exclusive definition of a trapezoid.

How to Understand the Result

The large result is area, not perimeter. The substitution and conversion rows help you check the arithmetic. Editing any field clears the previous result; calculate again. Try example fills the fields without silently calculating.

Common Mistakes

Do not enter a slanted side as the height or forget the division by two. Label the result in square units. The calculator does not derive missing sides, angles, coordinates or irregular boundaries.

FAQ

Which height should I enter?

Height is perpendicular to the bases, not the slanted side.

Do the bases need to be different lengths?

Yes. The same area formula also works when the bases have equal lengths.

Does changing units change the physical area?

No. Valid dimensions are converted to preserve their physical size.

Notes

Each numeric input is at most 1e9; converted dimensions are bounded at 1e−9 to 1e9 m and area at 1e−12 to 1e12 m². Results show at most six decimal places, using scientific notation for extreme magnitudes. Floating-point arithmetic is used. Inputs stay in page state. See the NIST length-conversion reference for unit definitions.