Calculate trapezium (trapezoid) area, perimeter, mid-segment (median), bases, and height with step-by-step mathematical steps.
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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.
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.
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
In British English, a trapezium has one pair of parallel sides. In American English, the exact same shape is called a trapezoid.
The mid-segment (or median) connects the midpoints of the two non-parallel legs. Its length is m = (a + b) / 2.
Perimeter is the sum of all four outer boundaries: P = a + b + c + d, where c and d are the legs.
A right trapezium has two adjacent right angles (one leg is perpendicular to both parallel bases).
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