Trapezoid Area Calculator

This trapezoid area calculator lets you compute the area of a trapezoid in several ways: from bases and height, from bases and equal leg for an isosceles trapezoid, or directly from the coordinates of the four vertices.

It also reports perimeter (when side lengths are known), the midsegment length, and the height (if it is derived instead of entered). Results are designed for both students and professionals who need fast and reliable geometric calculations.

1. Enter trapezoid dimensions

Choose input method

Provide both parallel bases \( b_1 \) and \( b_2 \), the height \( h \), and optionally the non-parallel sides \( c \) and \( d \) for the perimeter.

All dimensions must use the same linear unit

Trapezoid area – main formulas

A trapezoid (or trapezium in some regions) is a quadrilateral with at least one pair of parallel sides. Those parallel sides are called the bases, usually denoted \( b_1 \) and \( b_2 \). The distance between them is the height \( h \).

The fundamental area formula is

\[ A = \frac{(b_1 + b_2)\,h}{2}. \]

Intuitively, this is the area of a rectangle with height \( h \) and base equal to the average of the two bases:

\[ A = \overline{m}\,h, \quad \overline{m} = \frac{b_1 + b_2}{2}. \]

Isosceles trapezoid – bases and equal leg

In an isosceles trapezoid the non-parallel sides (legs) are equal: \( c = d = l \). If we know the two bases \( b_1 \leq b_2 \) and the leg \( l \), we can recover the height using Pythagoras.

The horizontal offset at each side is

\[ x = \frac{b_2 - b_1}{2}, \]

and the height is obtained from the right triangle:

\[ h = \sqrt{l^2 - x^2}, \]

assuming \( l \geq x \). Then the area follows from the main formula above. The perimeter is

\[ P = b_1 + b_2 + 2l. \]

Coordinates method – shoelace formula

If the vertices \( A(x_1,y_1), B(x_2,y_2), C(x_3,y_3), D(x_4,y_4) \) are known in order around the trapezoid, we can compute the area using the shoelace formula:

\[ A = \frac{1}{2}\left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right|. \]

The calculator also computes each side length using the Euclidean distance \[ \text{side length} = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}, \] and reports the perimeter whenever all four sides are well-defined.

Worked example – bases and height

Suppose a trapezoid has bases \( b_1 = 8\;\text{m} \), \( b_2 = 14\;\text{m} \), and height \( h = 5\;\text{m} \).

  1. Compute the midsegment: \( \overline{m} = (8 + 14)/2 = 11 \;\text{m} \).
  2. Compute the area: \( A = \overline{m}\,h = 11 \cdot 5 = 55\;\text{m}^2 \).

Entering these values into the calculator with unit meters returns an area of \( 55\;\text{m}^2 \), plus the chosen extra metrics if side lengths are supplied.

Trapezoid geometry – FAQ