Trapezoid Area Calculator
The trapezoid area formula, explained and computed: enter the two parallel bases and the height for the area with substitution steps.
How to use this calculator
Enter the lengths of the two parallel sides (a and b) and the height, the perpendicular distance between them, then press Calculate. The calculator applies A = (1/2)(a+b)h and shows each substitution.
How it works
A trapezoid is the average of its two bases times the height: A = (a+b)/2 × h. Why? Two copies of any trapezoid fit together into a parallelogram with base (a+b) and height h, so one trapezoid is half of that. The formula is just that picture, written down.
Worked example
Example: a = 3, b = 5, h = 4
Step 1, Average the bases: (3 + 5) ÷ 2 = 4.
Step 2, Times height: 4 × 4 = 16 square units.
Common mistakes
- Using a slanted side as h: height must be perpendicular to the bases, the slanted leg is longer and gives a wrong answer.
- Adding instead of averaging: (a+b)×h without the half computes the doubled parallelogram, not the trapezoid.
- Mixing up which sides are the bases: the bases are the parallel pair. In an isosceles trapezoid that is usually obvious; in a right trapezoid, check.
When to use it
Trapezoids appear in land plots, cross-sections of channels and dams, table tops, and the trapezoidal rule of numerical integration. Any four-sided figure with one pair of parallel sides answers to this formula.
Frequently asked questions
A = (1/2)(a + b)h, where a and b are the two parallel sides and h is the perpendicular distance between them.
The two parallel sides, by definition. The height is measured perpendicularly between them, not along a slanted leg.
Two identical trapezoids join into a parallelogram of area (a+b)h, so one trapezoid is half of that.
Yes, symmetry does not change the formula. As long as a and b are the parallel sides, A = (1/2)(a+b)h holds.