Trapezium Calculator
Calculate trapezium (trapezoid) area, perimeter, mid-segment (median), bases, and height with step-by-step mathematical steps.
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What Is a Trapezium Calculator?
A trapezium (known as a trapezoid in American English) is a four-sided convex quadrilateral with at least one pair of parallel sides, called the bases (a and b). The non-parallel sides are called legs.
How to Use This Calculator
- Enter parallel bases a and b, and the perpendicular height h.
- View the calculated Area, Mid-Segment (median), and estimated Perimeter.
- Review the step-by-step mathematical solution.
Trapezium Area & Mid-Segment Formulas
A = \frac{a + b}{2} \times h = m \times h, \quad m = \frac{a + b}{2}Area is the average of the two parallel bases multiplied by the perpendicular height. The average of bases is also the mid-segment m.
Worked Example
Scenario: Calculate area of a trapezium with bases a = 12 cm, b = 8 cm, height h = 6 cm
Mid-segment: m = (12 + 8) / 2 = 20 / 2 = 10 cm
Area: A = m × h = 10 × 6 = 60 cm²
Tips & Key Notes
- Height must be measured perpendicular to the parallel bases.
- An isosceles trapezium has non-parallel legs of equal length and symmetric base angles.
- The mid-segment is parallel to both bases and its length is their arithmetic mean.
Frequently Asked Questions
What is the difference between a trapezium and a trapezoid?
In British English, a trapezium has one pair of parallel sides. In American English, the exact same shape is called a trapezoid.
What is the mid-segment of a trapezium?
The mid-segment (or median) connects the midpoints of the two non-parallel legs. Its length is m = (a + b) / 2.
How do you find perimeter of a trapezium?
Perimeter is the sum of all four outer boundaries: P = a + b + c + d, where c and d are the legs.
What is a right trapezium?
A right trapezium has two adjacent right angles (one leg is perpendicular to both parallel bases).
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