Formula

A = (a + b) × h ÷ 2, where a and b are the parallel bases and h is the perpendicular height. If a = 8 ft, b = 14 ft and h = 5 ft, the area is 55 ft².

Identify the three dimensions

Trapezoid with upper base 8 feet, lower base 14 feet and perpendicular height 5 feeta = 8 ftb = 14 fth = 5 ft
Only the top and bottom edges are parallel. The red dashed segment is the perpendicular height, not a slanted leg.

Example 1: a straightforward trapezoid

The two parallel sides are 8 ft and 14 ft, and the height between them is 5 ft. First find the average length of the parallel sides: (8 + 14) ÷ 2 = 11 ft. Then multiply by the height:

Average base = (8 + 14) ÷ 2 = 11 ft

Area = 11 × 5 = 55 ft²

This result is independent of where the shorter top base sits horizontally. Sliding the top base without changing the height or the two parallel base lengths changes the angles but not the area.

Why does averaging the bases work?

Imagine placing a second identical trapezoid upside down alongside the first. The pair forms a parallelogram with base (a + b) and height h. That parallelogram covers area (a + b)h, and each of the two congruent trapezoids occupies half.

This geometric argument also shows why you cannot replace h with an angled side: the parallelogram's area depends on the perpendicular distance between its parallel sides.

Example 2: an isosceles trapezoid with no given height

Sometimes you know both parallel bases and the equal legs instead of the height. For an isosceles trapezoid with bases 12 cm and 6 cm and equal legs of 5 cm, the overhang on each side is (12 − 6) ÷ 2 = 3 cm. A right triangle at one end has hypotenuse 5 cm and horizontal leg 3 cm.

h = √(5² − 3²) = √16 = 4 cm

A = ((12 + 6) ÷ 2) × 4

A = 36 cm²

This shortcut relies on the trapezoid being isosceles. It is not a universal way to derive height for any four-sided shape.

Before you trust your answer

  • Confirm parallelism: the two values you average must describe the parallel sides.
  • Measure a right angle: h is perpendicular to both bases.
  • Use a single unit: convert meters and centimeters before substituting values.
  • Check magnitude: area should lie between min(a,b) × h and max(a,b) × h.

Try your dimensions in the trapezoid mode on the homepage. For other familiar formulas, read the triangle area explanation.

Formula reference: OpenStax, chapter 10 formula review.

How this guide was prepared. Formulas and example calculations are shown explicitly so you can verify them. Measurements are illustrative; the About page explains the tool’s scope.