Theory:

A trapezium or a trapezoid is a quadrilateral with a pair of parallel sides. A parallelogram has also be called a trapezoid as it has two parallel sides.
  • The pair of parallel sides have called the base while the non-parallel sides are called the legs of the trapezium.
  • The line segment that connects the midpoints of the legs of a trapezium is called the mid-segment.
Trapezium.png
Properties of a Trapezium:
  • The diagonals of trapezium bisect each other.
  • A Trapezium has two parallel sides and two non-parallel sides.
  • A Trapezium has four unequal sides.
  • Like other quadrilaterals, the sum of all the four angles of the trapezium is equal to  360 degrees.
  • No sides, angles and diagonals of the trapezium are congruent.
  • The length of the mid-segment is equal to 1/2 the sum of the parallel bases, in a trapezium.
Trapezium Applications
The concept of the trapezium has highly used in  various physics computations and other mathematical calculations.
 
Trapezoid & Trapezium
In the US and UK, Trapezoid and Trapezium have differentiated as below.
 
      
 
Trapezoid
Trapezium
US
A quadrilateral with a pair of parallel sides.
A quadrilateral with no parallel sides.
UK
A quadrilateral with no parallel sides.
A quadrilateral with a pair of parallel sides.