Trapezoid Area Formula Calculator

Area of a trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides, the major base B and the minor base b, held apart by the height h. Its area comes out to A = (B + b)·h / 2, which is the same as A = m·h once you set m = (B + b)/2, the median that joins the midpoints of the non-parallel sides. Here's the picture behind it: copy the trapezoid, rotate the copy, and the two together make a parallelogram of base (B + b) and height h. Take half of that parallelogram and you're back to the original area. For B = 10, b = 6 and h = 4: A = (10 + 6)·4/2 = 32.

Applications

Numerical integration leans on the trapezoidal rule, which estimates a definite integral by adding up thin trapezoids tucked under the curve. Surveying slices irregular plots into trapezoidal strips and reads off the land area from cross-sectional measurements. And in hydraulic engineering the same formula gives the wetted cross-section of trapezoidal channels used in irrigation, drainage and sanitary sewers.

FAQ

What is the median of the trapezoid? It's the segment that joins the midpoints of the two non-parallel sides. Its length is the arithmetic mean (B + b)/2, and it runs parallel to the bases.

Does the formula work for an oblique trapezoid? Yes. The height h is always the perpendicular distance between the parallel sides, regardless of how the lateral sides lean.

Is the height the slant side? No. Height is the perpendicular gap between the two bases. If all you have is the slant side, fall back on trigonometry or Pythagoras to pull out h.