Trapezoid Calculator
This trapezoid calculator finds area, height, midsegment, perimeter and diagonals from three or four known measures and shows the working, for any trapezoid including isosceles ones.
Example: Unit: cm · Base a (long) 10 · Base c (short) 4 · Height h 4 → Area: Area A = 28 cm² (midsegment m = 7 cm). Source: Wikipedia – Trapez (Geometrie): area, midline, and height from the four sides. Updated: .
How it is calculated
A trapezoid with bases 10 cm and 4 cm and a height of 4 cm has an area of 28 cm². The area is the midsegment times the height: A = (a + c) / 2 · h.
How it works
A trapezoid (trapezium in British English) has two parallel sides, the bases a and c, and two legs b and d. The midsegment m = (a + c) / 2 runs halfway between the bases. The calculator takes what you know and solves for the rest: from a, c and the area it finds the height, from area, height and one base the other base, and from all four sides the height via the triangle with sides a − c, b and d.
Good to know
- Isosceles means b = d: then a, c and h are enough, and you also get the legs and the two equal diagonals.
- In a right trapezoid one leg stands at 90° to the bases, so that leg is also the height (b = h).
- If the height is unknown, an isosceles trapezoid needs only a leg: h = √(b² − ((a − c) / 2)²).
- With equal bases (a = c) you get a parallelogram, and the same area formula applies.
Frequently asked questions
How do you find the area of a trapezoid?
Use A = (a + c) / 2 · h: add the two bases, divide by 2 and multiply by the height.
How do you find a trapezoid without the height?
With all four sides known, the height follows from the triangle with sides a − c, b and d. For an isosceles trapezoid one leg is enough. If you know the area, h = 2 · A / (a + c).
How do you calculate an isosceles trapezoid?
Tick the isosceles box and enter a, c and h. The leg is √(h² + ((a − c) / 2)²) and the perimeter is a + c + 2 · leg.
What is the midsegment of a trapezoid?
The segment joining the midpoints of the two legs. It is parallel to the bases and as long as their average, (a + c) / 2.
Sources and legal basis
- Wikipedia – Trapez (Geometrie): area, midline, and height from the four sides
- Wolfram MathWorld – Trapezoid (area, height from the four sides)
- Wikipedia – Trapezoid (formulas for height and diagonals)
As of: · Editorial policy
Related tools
- Square Footage CalculatorSquare footage calculator for rooms and whole homes: enter feet and inches or metres, add rooms and L-shapes, get sq ft, m², sq yd, acres, waste and cost.
- Triangle CalculatorTriangle calculator from any three values (SSS, SAS, ASA, AAS, SSA): missing sides and angles, area, perimeter, heights, inradius and circumradius.
- Regular polygon calculatorRegular polygon calculator for 3 to 1000 sides from side length, circumradius, inradius or area: area, perimeter, radii, angles and diagonals with formulas.
- Parallelogram calculatorParallelogram calculator from two sides and an angle – rhombus too, from a side and angle or both diagonals: area, perimeter, heights, diagonals with formulas.
- Circumference CalculatorCircumference calculator that also gives perimeter and area of a circle, rectangle, square, ellipse, triangle, trapezoid, parallelogram or polygon.
- Pythagorean Theorem CalculatorPythagorean theorem calculator: enter two sides to get the third side, both angles, area and height – with exact square roots, working and a right-angle check.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Rhombus CalculatorRhombus calculator from side and angle, both diagonals, side and diagonal, or area and side: perimeter, area, height, incircle radius and angles with steps.
- Kite Area CalculatorKite area calculator for the geometric kite: from diagonals, from sides and symmetry axis or from sides and angle, with perimeter, angles and steps.