How to Calculate the Area of a Trapezoid
This calculator applies the trapezoid area formula, one of the most common quadrilaterals in plane geometry and practical applications.
The Area Formula
The area of a trapezoid is calculated with:
A = (B + b) x h / 2
where B is the longer base, b is the shorter base, and h is the height (the perpendicular distance between the two parallel bases).
The formula can be interpreted as: the area equals the arithmetic mean of the two bases multiplied by the height.
Why This Formula Works
The most intuitive proof: take two identical trapezoids and place the second, rotated 180 degrees, alongside the first. You get a parallelogram with base (B + b) and height h, whose area is (B + b) x h. The original trapezoid is exactly half of this parallelogram.
Types of Trapezoids
- Right trapezoid: has one side perpendicular to the bases (two right angles)
- Isosceles trapezoid: the two non-parallel sides are equal, with an axis of symmetry
- Scalene trapezoid: all sides have different measures
In all cases, the area formula remains the same: what matters are only the two parallel bases and the height.
Practical Applications
The trapezoid appears frequently in construction (inclined wall sections, roof slopes), land surveying (surfaces with parallel sides), hydraulic engineering (channel cross-sections), and numerical mathematics (the trapezoidal rule for approximate integration).