Area of a Trapezium

In the adjoining figure, the side AB (a) and CD (b) of trapezium ABCD are parallel to each other. AE = BG = h is the height of the trapezium and AC is the diagonal.

Area of trapezium (A) = Area of △ADC + Area of △ABC
=
12 CD × AE + 12 AB × BG
=
12 b × h + 12 a × h
=
12 h × (a + b)
Hence,
Area of trapezium = 12 h × (a + b)
=
12 height × sum of parallel sides