Irregular Trapezoid Area Calculator

Calculate the area of an irregular trapezoid with unequal non-parallel sides using dimensions or coordinates.

Select Input Method

Result

Area
40
square units
Parallel side a 6
Parallel side b 10
Height 5
Perimeter --

Step-by-Step Solution

A = (a + b) / 2 * h

Understanding Irregular Trapezoids

An irregular trapezoid (also called a scalene trapezoid) is a quadrilateral with exactly one pair of parallel sides where the non-parallel sides (legs) have different lengths. Unlike an isosceles trapezoid where the legs are equal, an irregular trapezoid has legs of unequal length, making it asymmetric.

Area Formulas

Using Parallel Sides & Height

The most common formula, applicable when you know both parallel sides and the perpendicular height.

A = (a + b) / 2 * h

Using All 4 Sides

When the height is unknown, compute it from the four side lengths using the Pythagorean theorem.

h = sqrt(c^2 - ((b-a)^2+c^2-d^2)/(2(b-a)))^2)

Using Coordinates

Apply the Shoelace formula to the four vertex coordinates to find the area directly.

A = |x1(y2-y4) + x2(y3-y1) + ...| / 2

Irregular vs. Isosceles Trapezoid

The key difference is symmetry. An isosceles trapezoid has equal legs, equal base angles, and a line of symmetry. An irregular trapezoid has unequal legs, unequal base angles, and no line of symmetry. Both share the same area formula when the parallel sides and height are known.

Properties of an Irregular Trapezoid

  • Exactly one pair of parallel sides (called bases).
  • Two non-parallel sides (legs) of different lengths.
  • The sum of interior angles is 360 degrees.
  • Co-interior angles between a leg and the two bases sum to 180 degrees.
  • The diagonals have different lengths (unlike isosceles trapezoids).
  • The midsegment (median) length equals the average of the two parallel sides: m = (a + b) / 2.

Computing Height from Four Sides

When you know all four side lengths (a, b, c, d) of a trapezoid where a and b are parallel (a < b), you can find the height using the relationship between the legs and the difference in base lengths. Place the trapezoid on a coordinate system with the longer base along the x-axis. The left foot of the shorter base is at horizontal distance p from the left end of the longer base, and the height h satisfies both c² = p² + h² and d² = (b - a - p)² + h².

How to Use This Calculator

  1. Parallel Sides + Height: Enter the two parallel sides and the perpendicular height.
  2. All 4 Sides: Enter both parallel sides and both legs; the calculator determines the height.
  3. Coordinates: Enter the four vertices; the Shoelace formula computes the area.