Trapezoid Area Calculator
Trapezoid area calculator with multiple methods. Compute area from bases and height, isosceles trapezoid sides, or coordinates of vertices. Get perimeter, midsegment, height and step-by-step formulas.
Full original guide (expanded)
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.
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
Intuitively, this is the area of a rectangle with height \( h \) and base equal to the average of the two bases:
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
and the height is obtained from the right triangle:
assuming \( l \geq x \). Then the area follows from the main formula above. The perimeter is
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:
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 \( h = 5\;\text{m} \).
- Compute the midsegment: \( \overline{m} = (8 + 14)/2 = 11 \;\text{m} \).
- 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
Formula (LaTeX) + variables + units
A = \frac{(b_1 + b_2)\,h}{2}.
A = \overline{m}\,h, \quad \overline{m} = \frac{b_1 + b_2}{2}.
x = \frac{b_2 - b_1}{2},
h = \sqrt{l^2 - x^2},
P = b_1 + b_2 + 2l.
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|.
\[ A = \frac{(b_1 + b_2)\,h}{2}. \]
\[ A = \overline{m}\,h, \quad \overline{m} = \frac{b_1 + b_2}{2}. \]
\[ x = \frac{b_2 - b_1}{2}, \]
\[ h = \sqrt{l^2 - x^2}, \]
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.