Theory:

Area of trapezium: To obtain the area of a trapezium, multiply the sum of the bases by the height and then divide by \(2\).
  
The area of a trapezium is computed with the following formula:
 
area.PNG
 
Area of trapezium \(=\) 12×(a+b)×(h) square units.
 
(where \(a\) and \(b\) is bases (parallel sides) and \(h\) is leg or height (between the non-parallel sides)).
 
Area of the trapezium \(ABCD\):
 
Proof: Area of a trapezium \(ABCD\).
 
Area of trapezium \(ABCD\) \(=\) 12AB+DC×(h) \(square units\).
 
\(=\) area of triangle (DEA) \(+\) area of rectangle (DEFC) \(+\) area of triangle (CFB)
 
\(=\) 12×AE×DE \(+\) DE×EF \(+\) 12×FB×CF
 
\(=\) 12×AE×h \(+\) h×EF \(+\) 12×FB×h
 
\(=\) 12×(AE+2EF+FB)×h
 
\(=\) 12×(AE+EF+CD+FB)×h
 
\(=\) 12×(AE+EF+FB+CD)×h
 
\(=\) 12×(AB+CD)×h
 
\(=\) 12×(a+b)×(h)

\(=\) \(\frac{1}{2}\times\)(\(\text{sum of parallel side}\)) \(\times\)\((\text{height})\) square units.
 
Therefore, Area of trapezium \(ABCD =\) 12×(a+b)×(h) or
 
Perimeter of trapezium: The Perimeter is the sum of all side lengths.
 
The perimeter of a trapezium is computed with the following formula:
 
perimeter.PNG
 
Perimeter of trapezium \(=\) \(a + b + c + d\) (where \(a\), \(b\) are denoted as bases (parallel sides) and \(c\), \(d\) are denoted as legs (non-parallel sides)).